The.Algorithm.Design.Manual.Springer-Verlag.1998

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Planarity Detection and Embedding The study of planarity has motivated much of the development of graph theory. To get a better appreciation of the subtleties of planar drawings, the reader is urged to construct a planar (noncrossing) embedding for the graph , the complete graph on five vertices with any single edge deleted. Then construct such an embedding where all the edges are straight. Finally, attempt to do the same for itself. It is useful to distinguish the problem of planarity testing (does a graph have a planar drawing) from constructing planar embeddings (actually finding the drawing), although both can be done in linear time. Surprisingly, many efficient algorithms for planar graphs do not make use of the drawing but use the low-degree deletion sequence described above. Algorithms for planarity testing begin by embedding an arbitrary cycle from the graph in the plane and then considering additional paths in G between vertices on this cycle. Whenever two such paths cross, one must be drawn outside the cycle and one inside. When three such paths mutually cross, there is no way to resolve the problem, and so the graph cannot be planar. Linear-time algorithms for planarity detection are based on depth-first search, but they are subtle and complicated enough that you would be wise to use an existing implementation if you can. Such path-crossing algorithms can be used to construct a planar embedding by inserting the paths into the drawing one by one. Unfortunately, because they work in an incremental manner, nothing prevents them from inserting many vertices and edges into a relatively small area of the drawing. Such cramping makes the drawing ugly and hard to understand, and is a major problem with planar-embedding algorithms. More recently, algorithms have been devised that construct planar-grid embeddings, where each vertex lies on a grid. Thus no region can get too cramped and no edge can get too long. Still, the resulting drawings tend not to look as natural as one might hope. For nonplanar graphs, what is often sought is a drawing that minimizes the number of crossings. Unfortunately, computing the crossing number is NP-complete. A useful heuristic extracts a large planar subgraph of G, embeds this subgraph, and then inserts the remaining edges one by one so as to minimize the number of crossings. This won't do much for dense graphs, which are doomed to have a large number of crossings, but it will work well for graphs that are almost planar, such as road networks with overpasses or printed circuit boards with multiple layers. Large planar subgraphs can be found by modifying planarity-testing algorithms to delete troublemaking edges. Implementations: LEDA (see Section ) provides a nice set of data structures and algorithms to support working on planar subdivisions. Included are both linear-time planarity testing and constructing straight-line planar-grid embeddings. GraphEd includes an implementation of both planarity testing and planar graph layout. See Section for more details on GraphEd. Combinatorica [Ski90] provides a (slow) Mathematica implementation of file:///E|/BOOK/BOOK4/NODE170.HTM (2 of 3) [19/1/2003 1:31:14]
Planarity Detection and Embedding planarity testing. See Section . Notes: Kuratowski [Kur30] gave the first characterization of planar graphs, namely that they do not contain a subgraph homeomorphic to or . Thus if you are still working on the exercise to embed , now is an appropriate time to give it up. Fary's theorem [F48] states that every planar graph can be drawn such that each edge is straight. Hopcroft and Tarjan [HT74] gave the first linear-time algorithm for drawing graphs. Expositions on linear-time planarity testing include [Eve79a]. Nishizeki and Chiba [NC88] provide a good reference to the algorithmic theory of planar graphs. Efficient algorithms for planar grid embeddings were first developed by [dFPP88]. See [CHT90] for an algorithm to find the maximum planar subgraph of a nonplanar graph. Outerplanar graphs are those that can be drawn such that all vertices lie on the outer face of the drawing. Such graphs can be characterized as having no subgraph homeomorphic to and can be recognized and embedded in linear time. Related Problems: Graph partition (see page ), drawing trees (see page ). Next: Graph Problems: Hard Problems Up: Graph Problems: Polynomial-Time Previous: Drawing Trees Algorithms Mon Jun 2 23:33:50 EDT 1997 file:///E|/BOOK/BOOK4/NODE170.HTM (3 of 3) [19/1/2003 1:31:14]
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The Algorithm Design Manual Next: P
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Preface Next: Acknowledgments Up: T
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Preface one stressing design over a
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Acknowledgments Mon Jun 2 23:33:50
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Contents Next: Techniques Up: The A
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Contents ■ All-Pairs Shortest Pat
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Contents ■ Graph Problems: Polyno
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Contents ● About this document ..
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The Algorithm Design Manual The Alg
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Lecture Notes -- Analysis of Algori
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Lecture Notes -- Analysis of Algori
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The Stony Brook Algorithm Repositor
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Techniques Next: Introduction to Al
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Techniques Algorithms Mon Jun 2 23:
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Introduction to Algorithms ● Reas
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Data Structures and Sorting divide-
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Breaking Problems Down ● Dynamic
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Graph Algorithms The take-home less
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Combinatorial Search and Heuristic
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Intractable Problems and Approximat
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How to Design Algorithms Next: Reso
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How to Design Algorithms with a cou
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How to Design Algorithms Next: Reso
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A Catalog of Algorithmic Problems N
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A Catalog of Algorithmic Problems
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Algorithmic Resources Next: Softwar
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References L. Adleman. Algorithmic
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References AS89 Ata83 Ata84 problem
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References BJL 91 A. Blum, T. Jiang
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References BS81 BS86 BS93 BS96 BS97
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References J. M. Chambers. Partial
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References CT80 CT92 1971. G. Carpa
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References K. Daniels and V. Milenk
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References (FOCS), pages 60-69, 199
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References FM71 M. Fischer and A. M
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References History of Computing, 7:
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References N. Gibbs, W. Poole, and
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References Hof82 Hof89 Hol75 C. M.
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References IK75 Ita78 O. Ibarra and
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References Kir83 D. Kirkpatrick. Ef
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References object in 2-dimensional
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References LT79 LT80 8:99-118, 1995
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References Mil97 V. Milenkovic. Dou
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References Theoretical Computer Sci
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References Pav82 T. Pavlidis. Algor
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References Rei72 Rei91 Rei94 E. Rei
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References Prentice Hall, Englewood
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References SR95 SS71 SS90 SSS74 ST8
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References Tin90 Mikkel Thorup. On
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References Wel84 T. Welch. A techni
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References Algorithms Mon Jun 2 23:
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Correctness and Efficiency Next: Co
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Correctness NearestNeighborTSP(P) P
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Correctness Figure: A bad example f
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Efficiency Next: Expressing Algorit
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Keeping Score Next: The RAM Model o
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The RAM Model of Computation substa
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Best, Worst, and Average-Case Compl
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The Big Oh Notation Figure: Illustr
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Logarithms Next: Modeling the Probl
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Logarithms justified in ignoring th
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Modeling the Problem Figure: Modeli
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About the War Stories Next: War Sto
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War Story: Psychic Modeling Next: E
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War Story: Psychic Modeling have pu
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War Story: Psychic Modeling Next: E
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Exercises (b) If I prove that an al
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Fundamental Data Types Next: Contai
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Containers Next: Dictionaries Up: F
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Dictionaries Next: Binary Search Tr
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Binary Search Trees BinaryTreeQuery
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Priority Queues Next: Specialized D
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Specialized Data Structures Next: S
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Sorting Next: Applications of Sorti
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Applications of Sorting Figure: Con
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Data Structures Next: Incremental I
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Incremental Insertion Next: Divide
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Randomization Next: Bucketing Techn
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Randomization Next: Bucketing Techn
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Bucketing Techniques Algorithms Mon
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War Story: Stripping Triangulations
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War Story: Stripping Triangulations
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War Story: Mystery of the Pyramids
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War Story: Mystery of the Pyramids
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War Story: String 'em Up We were co
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War Story: String 'em Up Figure: Su
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Exercises Next: Implementation Chal
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Exercises used to select the pivot.
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Dynamic Programming Next: Fibonacci
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Fibonacci numbers Next: The Partiti
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Fibonacci numbers Next: The Partiti
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The Partition Problem . What is the
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The Partition Problem Figure: Dynam
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Approximate String Matching Next: L
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Approximate String Matching The val
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Longest Increasing Sequence Will th
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Minimum Weight Triangulation Next:
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Limitations of Dynamic Programming
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War Story: Evolution of the Lobster
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War Story: Evolution of the Lobster
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War Story: What's Past is Prolog Ne
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War Story: What's Past is Prolog th
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War Story: Text Compression for Bar
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War Story: Text Compression for Bar
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Divide and Conquer Next: Fast Expon
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Fast Exponentiation Next: Binary Se
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Binary Search Next: Square and Othe
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Exercises whose denominations are ,
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The Friendship Graph Next: Data Str
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The Friendship Graph friendship gra
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Data Structures for Graphs linked t
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War Story: Getting the Graph ``Well
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Traversing a Graph Next: Breadth-Fi
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Breadth-First Search Next: Depth-Fi
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Depth-First Search Next: Applicatio
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Depth-First Search Next: Applicatio
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Connected Components Next: Tree and
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Two-Coloring Graphs Next: Topologic
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Topological Sorting Next: Articulat
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Modeling Graph Problems Next: Minim
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Modeling Graph Problems good line s
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Minimum Spanning Trees ● Prim's A
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Prim's Algorithm inserted edge (x,y
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Kruskal's Algorithm a tree of weigh
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Dijkstra's Algorithm Next: All-Pair
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All-Pairs Shortest Path Next: War S
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War Story: Nothing but Nets Next: W
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War Story: Nothing but Nets ``You a
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War Story: Dialing for Documents Ne
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War Story: Dialing for Documents If
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War Story: Dialing for Documents CO
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Exercises Prove the statement or gi
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Backtracking report it. kth element
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Constructing All Subsets Next: Cons
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Constructing All Paths in a Graph N
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Search Pruning Next: Bandwidth Mini
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Bandwidth Minimization immediately
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War Story: Covering Chessboards Nex
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War Story: Covering Chessboards att
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Heuristic Methods Mon Jun 2 23:33:5
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Simulated Annealing Return S then u
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Traveling Salesman Problem Next: Ma
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Independent Set Next: Circuit Board
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Neural Networks Next: Genetic Algor
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Genetic Algorithms Next: War Story:
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War Story: Annealing Arrays Next: P
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War Story: Annealing Arrays optimal
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Parallel Algorithms Next: War Story
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War Story: Going Nowhere Fast Next:
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Problems and Reductions Next: Simpl
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Simple Reductions Next: Hamiltonian
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Hamiltonian Cycles Next: Independen
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Independent Set and Vertex Cover pr
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Clique and Independent Set These la
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Satisfiability Mon Jun 2 23:33:50 E
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The Theory of NP-Completeness Next:
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3-Satisfiability where for , , , an
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Integer Programming Next: Vertex Co
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Integer Programming possible IP ins
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Vertex Cover reduction for the 3-SA
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Other NP-Complete Problems hard. Th
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The Art of Proving Hardness easiest
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War Story: Hard Against the Clock N
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War Story: Hard Against the Clock I
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Approximation Algorithms Next: Appr
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Approximating Vertex Cover Next: Th
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The Euclidean Traveling Salesman Ne
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The Euclidean Traveling Salesman Ne
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Exercises 1. Prove that the low deg
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Data Structures Next: Dictionaries
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Dictionaries Next: Priority Queues
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Dictionaries use a function that ma
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Dictionaries Implementation-oriente
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Priority Queues ● Besides access
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Priority Queues Fibonacci heaps [FT
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Suffix Trees and Arrays Figure: A t
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Suffix Trees and Arrays [GBY91]. Se
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Graph Data Structures algorithms).
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Graph Data Structures including the
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Set Data Structures Next: Kd-Trees
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Set Data Structures parent pointers
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Kd-Trees Next: Numerical Problems U
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Kd-Trees about p. Say we are lookin
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Numerical Problems Next: Solving Li
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Numerical Problems Mon Jun 2 23:33:
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Solving Linear Equations algorithm
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Solving Linear Equations Matrix inv
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Bandwidth Reduction images near eac
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Matrix Multiplication Next: Determi
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Matrix Multiplication The linear al
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Determinants and Permanents Next: C
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Determinants and Permanents exposit
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Constrained and Unconstrained Optim
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Constrained and Unconstrained Optim
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Linear Programming variable assignm
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Linear Programming The book [MW93]
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Random Number Generation Next: Fact
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Random Number Generation is largely
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Random Number Generation Related Pr
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Factoring and Primality Testing The
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Factoring and Primality Testing Alg
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Arbitrary-Precision Arithmetic If y
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Arbitrary-Precision Arithmetic PARI
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Knapsack Problem Next: Discrete Fou
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Knapsack Problem is a subset of S'
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Discrete Fourier Transform Next: Co
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Discrete Fourier Transform an algor
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Combinatorial Problems Next: Sortin
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Sorting Next: Searching Up: Combina
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Sorting The simplest approach to ex
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Sorting operations, implying an sor
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Searching large performance improve
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Searching Notes: Mehlhorn and Tsaka
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Median and Selection followed by fi
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Generating Permutations Next: Gener
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Generating Permutations The rank/un
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Generating Permutations generating
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Generating Subsets look right when
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Generating Subsets above for detail
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Generating Partitions Although the
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Generating Partitions Two related c
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Generating Graphs generate: ● Do
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Generating Graphs Combinatorica [Sk
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Calendrical Calculations Next: Job
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Calendrical Calculations Gregorian,
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Job Scheduling ● To assign a set
Page 459 and 460: Job Scheduling shop scheduling incl
Page 461 and 462: Satisfiability logic, and automatic
Page 463 and 464: Satisfiability Next: Graph Problems
Page 465 and 466: Graph Problems: Polynomial-Time rec
Page 467 and 468: Connected Components Testing the co
Page 469 and 470: Connected Components discussing gra
Page 471 and 472: Topological Sorting contradiction t
Page 473 and 474: Minimum Spanning Tree Next: Shortes
Page 475 and 476: Minimum Spanning Tree help you sort
Page 477 and 478: Shortest Path Next: Transitive Clos
Page 479 and 480: Shortest Path easier to program tha
Page 481 and 482: Shortest Path Related Problems: Net
Page 483 and 484: Transitive Closure and Reduction
Page 485 and 486: Transitive Closure and Reduction Al
Page 487 and 488: Matching augmenting paths and stopp
Page 489 and 490: Matching Combinatorica [Ski90] prov
Page 491 and 492: Eulerian Cycle / Chinese Postman ar
Page 493 and 494: Eulerian Cycle / Chinese Postman Ne
Page 495 and 496: Edge and Vertex Connectivity Severa
Page 497 and 498: Edge and Vertex Connectivity Next:
Page 499 and 500: Network Flow programming model for
Page 501 and 502: Network Flow Combinatorica [Ski90]
Page 503 and 504: Drawing Graphs Nicely vertices are
Page 505 and 506: Drawing Graphs Nicely labs.com/orgs
Page 507 and 508: Drawing Trees such as the map of th
Page 509: Planarity Detection and Embedding N
Page 513 and 514: Graph Problems: Hard Problems ● C
Page 515 and 516: Clique approximate even to within a
Page 517 and 518: Independent Set Next: Vertex Cover
Page 519 and 520: Independent Set Related Problems: C
Page 521 and 522: Vertex Cover Vertex cover and indep
Page 523 and 524: Traveling Salesman Problem Next: Ha
Page 525 and 526: Traveling Salesman Problem practice
Page 527 and 528: Traveling Salesman Problem Size is
Page 529 and 530: Hamiltonian Cycle Eulerian cycle, p
Page 531 and 532: Graph Partition Next: Vertex Colori
Page 533 and 534: Graph Partition annealing, is almos
Page 535 and 536: Vertex Coloring Several special cas
Page 537 and 538: Vertex Coloring Notes: An excellent
Page 539 and 540: Edge Coloring The minimum number of
Page 541 and 542: Graph Isomorphism Next: Steiner Tre
Page 543 and 544: Graph Isomorphism vertices into equ
Page 545 and 546: Steiner Tree Next: Feedback Edge/Ve
Page 547 and 548: Steiner Tree The worst case for a m
Page 549 and 550: Feedback Edge/Vertex Set Next: Comp
Page 551 and 552: Feedback Edge/Vertex Set An interes
Page 553 and 554: Computational Geometry complete bib
Page 555 and 556: Robust Geometric Primitives Next: C
Page 557 and 558: Robust Geometric Primitives ● Are
Page 559 and 560: Robust Geometric Primitives Related
Page 561 and 562:
Convex Hull ● How many dimensions
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Convex Hull http://www.cs.att.com/n
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Triangulation Next: Voronoi Diagram
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Triangulation GEOMPACK is a suite o
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Voronoi Diagrams Next: Nearest Neig
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Voronoi Diagrams McDonald's, the ti
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Nearest Neighbor Search Next: Range
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Nearest Neighbor Search Implementat
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Range Search Next: Point Location U
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Range Search subdivisions in C++. I
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Point Location the n edges for inte
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Point Location More recently, there
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Intersection Detection ● Do you w
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Intersection Detection Implementati
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Bin Packing Next: Medial-Axis Trans
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Bin Packing approach for general sh
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Medial-Axis Transformation Next: Po
Page 595 and 596:
Medial-Axis Transformation Implemen
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Polygon Partitioning number of piec
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Simplifying Polygons Next: Shape Si
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Simplifying Polygons vertices and o
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Shape Similarity Next: Motion Plann
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Shape Similarity or how close it is
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Motion Planning There is a wide ran
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Motion Planning often arise in the
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Maintaining Line Arrangements Think
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Maintaining Line Arrangements Next:
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Minkowski Sum where x+y is the vect
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Set and String Problems Next: Set C
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Set Cover Next: Set Packing Up: Set
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Set Cover Figure: Hitting set is du
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Set Packing Next: String Matching U
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Set Packing Notes: An excellent exp
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String Matching shouldn't try. Furt
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String Matching and texts, I recomm
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Approximate String Matching This sa
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Approximate String Matching http://
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Text Compression Next: Cryptography
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Text Compression code string. ASCII
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Cryptography Next: Finite State Mac
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Cryptography ● How can I validate
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Cryptography MD5 [Riv92] is the sec
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Finite State Machine Minimization F
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Finite State Machine Minimization S
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Longest Common Substring than edit
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Longest Common Substring include [A
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Shortest Common Superstring Finding
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Software systems Next: LEDA Up: Alg
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LEDA Next: Netlib Up: Software syst
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Netlib Algorithms Mon Jun 2 23:33:5
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The Stanford GraphBase Next: Combin
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Algorithm Animations with XTango Ne
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Programs from Books Next: Discrete
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Handbook of Data Structures and Alg
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Algorithms from P to NP Next: Compu
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Algorithms in C++ Next: Data Source
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Textbooks Next: On-Line Resources U
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On-Line Resources Next: Literature
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People Next: Software Up: On-Line R
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Professional Consulting Services Ne
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Index A Up: Index - All Index: A ab
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Index A artists steal ASA ASCII asp
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Index B binary representation - sub
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Index C Up: Index - All Index: C C+
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Index C clustering , , co-NP coding
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Index C consulting services , conta
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Index D Up: Index - All Index: D DA
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Index D Dictionaries dictionaries -
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Index D dynamic programming - appli
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Index E empirical results - heurist
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Index F Up: Index - All Index: F fa
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Index F frequency domain friend-or-
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Index G geometric shortest path , g
Page 707 and 708:
Index H Up: Index - All Index: H ha
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Index H Algorithms Tue Jun 3 11:59:
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Index I independent set - alternate
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Index J Up: Index - All Index: J ji
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Index K Algorithms Tue Jun 3 11:59:
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Index L linear congruential generat
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Index M Up: Index - All Index: M ma
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Index M mindset minima minimax sear
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Index N Up: Index - All Index: N na
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Index N numerical analysis numerica
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Index O overlap graph overpasses -
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Index P , , , , , , , , , , passwor
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Index P polygons polygon triangulat
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Index Q Up: Index - All Index: Q Qh
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Index R ranking combinatorial objec
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Index S Up: Index - All Index: S s-
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Index S Shape Similarity shape simp
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Index S solar year Solving Linear E
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Index S straight-line graph drawing
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Index T Up: Index - All Index: T ta
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Index T trees - matching trees - pa
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Index V Up: Index - All Index: V va
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Index W Up: Index - All Index: W wa
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Index Y Up: Index - All Index: Y Yo
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Index (complete) Up: Index - All In
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Index (complete) arm, robot around
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Index (complete) binary search tree
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Index (complete) center vertex, , C
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Index (complete) compaction compari
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Index (complete) counting paths, co
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Index (complete) deletion from bina
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Index (complete) dominance ordering
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Index (complete) English to French
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Index (complete) file directory tre
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Index (complete) geom.bib, geometri
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Index (complete) Hamiltonian Cycle
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Index (complete) implementation cha
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Index (complete) job-shop schedulin
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Index (complete) linear programming
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Index (complete) , , , , , , , math
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Index (complete) modular arithmetic
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Index (complete) normal distributio
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Index (complete) parallel algorithm
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Index (complete) planar subdivision
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Index (complete) proof of correctne
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Index (complete) regular expression
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Index (complete) self-organizing tr
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Index (complete) sine functions sin
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Index (complete) spring embedding h
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Index (complete) Symbol Technologie
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Index (complete) trial division Tri
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Index (complete) VLSI circuit layou
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1.4.4 Shortest Path 1.4.4 Shortest
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1.2.5 Constrained and Unconstrained
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1.6.4 Voronoi Diagrams 1.6.4 Vorono
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1.4.7 Eulerian Cycle / Chinese Post
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Online Bibliographies Online Biblio
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About the Book -- The Algorithm Des
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Copyright and Disclaimers Copyright
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CD-ROM Installation Installation an
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CD-ROM Installation install a sound
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Thanks! Frank Ruscica file:///E|/WE
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Thanks! Zhong Li Thanks also to Fil
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CD-ROM Installation To use the CD-R
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Binary Search in Action Binary Sear
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Binary Search in Action file:///E|/
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Binary Search in Action file:///E|/
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Postscript version of the lecture n
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Lecture 1 - analyzing algorithms Ne
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Lecture 1 - analyzing algorithms Yo
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Lecture 1 - analyzing algorithms Th
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Lecture 1 - analyzing algorithms Th
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Lecture 1 - analyzing algorithms is
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Lecture 2 - asymptotic notation How
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Lecture 2 - asymptotic notation Not
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Lecture 2 - asymptotic notation alg
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Lecture 2 - asymptotic notation Sup
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Lecture 2 - asymptotic notation Nex
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Lecture 3 - recurrence relations Is
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Lecture 3 - recurrence relations
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Lecture 3 - recurrence relations Li
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Lecture 3 - recurrence relations Su
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Lecture 3 - recurrence relations A
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Lecture 4 - heapsort Note iteration
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Lecture 4 - heapsort The convex hul
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Lecture 4 - heapsort 1. All leaves
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Lecture 4 - heapsort left = 2i righ
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Lecture 4 - heapsort Since this sum
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Lecture 4 - heapsort Selection sort
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Lecture 4 - heapsort Greedy Algorit
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Lecture 5 - quicksort Partitioning
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Lecture 5 - quicksort Listen To Par
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Lecture 5 - quicksort Listen To Par
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Lecture 5 - quicksort The worst cas
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Lecture 5 - quicksort Mon Jun 2 09:
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Lecture 6 - linear sorting Since 2i
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Lecture 6 - linear sorting With uni
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Lecture 6 - linear sorting Listen T
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Lecture 7 - elementary data structu
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Lecture 8 - binary trees - Joyce Ki
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Lecture 8 - binary trees TREE-MINIM
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Lecture 8 - binary trees Inorder-Tr
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Lecture 8 - binary trees Listen To
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Lecture 8 - binary trees insert(b)
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Lecture 8 - binary trees Not (1) -
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Lecture 9 - catch up Next: Lecture
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Lecture 10 - tree restructuring 1.
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Lecture 10 - tree restructuring Lis
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Lecture 10 - tree restructuring Not
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Lecture 10 - tree restructuring Cas
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Lecture 11 - backtracking Next: Lec
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Lecture 11 - backtracking Only 63 s
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Lecture 11 - backtracking Recursion
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Lecture 11 - backtracking Specifica
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Lecture 12 - introduction to dynami
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Lecture 13 - dynamic programming ap
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Lecture 14 - data structures for gr
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Lecture 15 - DFS and BFS Next: Lect
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Lecture 15 - DFS and BFS In a DFS o
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Lecture 15 - DFS and BFS It could u
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Lecture 15 - DFS and BFS Algorithm
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Lecture 16 - applications of DFS an
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Lecture 17 - minimum spanning trees
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Lecture 18 - shortest path algorthm
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Lecture 19 - satisfiability Next: L
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Lecture 19 - satisfiability Why? Th
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Lecture 19 - satisfiability between
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Lecture 19 - satisfiability Note th
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Lecture 20 - integer programming Ex
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Lecture 20 - integer programming Ne
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Lecture 21 - vertex cover Proof: VC
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Lecture 21 - vertex cover Question:
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Lecture 21 - vertex cover seen to d
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Lecture 22 - techniques for proving
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Lecture 23 - approximation algorith
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About this document ... Up: No Titl
Page 1047 and 1048:
1.1.6 Kd-Trees ● Point Location
Page 1049 and 1050:
1.1.3 Suffix Trees and Arrays Send
Page 1051 and 1052:
1.5.1 Clique ● Vertex Cover Go to
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1.6.2 Convex Hull Related Problems
Page 1055 and 1056:
Visual Links Index file:///E|/WEBSI
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About the Ratings About the Ratings
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1.2 Numerical Problems 1.2 Numerica
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1.4 Graph Problems -- polynomial-ti
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1.6 Computational Geometry 1.6 Comp
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C++ Language Implementations Algori
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C Language Implementations ● POSI
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FORTRAN Language Implementations Al
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Lisp Language Implementations Algor
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Algorithm Repository -- Citations C
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Practical Algorithm Design -- User
Page 1103 and 1104:
LEDA - A Library of Efficient Data
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Discrete Optimization Methods Discr
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Netlib / TOMS -- Collected Algorith
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Netlib / TOMS -- Collected Algorith
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Xtango and Polka Algorithm Animatio
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Combinatorica Combinatorica Combina
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file:///E|/WEBSITE/IMPLEMEN/GRAPHBA
Page 1117 and 1118:
1.4.1 Connected Components 1.4.1 Co
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1.5.9 Graph Isomorphism 1.5.9 Graph
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1.2.3 Matrix Multiplication 1.2.3 M
Page 1123 and 1124:
1.6.14 Motion Planning 1.6.14 Motio
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1.4.9 Network Flow 1.4.9 Network Fl
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1.1.2 Priority Queues 1.1.2 Priorit
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1.5.10 Steiner Tree 1.5.10 Steiner
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1.4.5 Transitive Closure and Reduct
Page 1133 and 1134:
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Genocop -- Optimization via Genetic
Page 1139 and 1140:
1.2.6 Linear Programming ● Knapsa
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1.2.7 Random Number Generation ●
Page 1143 and 1144:
1.3.10 Satisfiability ● Constrain
Page 1145 and 1146:
Qhull - higher dimensional convex h
Page 1147 and 1148:
1.6.5 Nearest Neighbor Search 1.6.5
Page 1149 and 1150:
1.6.7 Point Location 1.6.7 Point Lo
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1.6.10 Medial-Axis Transformation 1
Page 1153 and 1154:
1.6.3 Triangulation 1.6.3 Triangula
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Nijenhuis and Wilf: Combinatorial A
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1.5.5 Hamiltonian Cycle 1.5.5 Hamil
Page 1159 and 1160:
1.4.6 Matching 1.4.6 Matching INPUT
Page 1161 and 1162:
A compendium of NP optimization pro
Page 1163 and 1164:
1.6.9 Bin Packing 1.6.9 Bin Packing
Page 1165 and 1166:
1.6.12 Simplifying Polygons 1.6.12
Page 1167 and 1168:
1.6.13 Shape Similarity 1.6.13 Shap
Page 1169 and 1170:
1.6.11 Polygon Partitioning 1.6.11
Page 1171 and 1172:
1.4.3 Minimum Spanning Tree 1.4.3 M
Page 1173 and 1174:
1.6.15 Maintaining Line Arrangement
Page 1175 and 1176:
1.3.7 Generating Graphs 1.3.7 Gener
Page 1177 and 1178:
1.2.11 Discrete Fourier Transform 1
Page 1179 and 1180:
1.5.8 Edge Coloring 1.5.8 Edge Colo
Page 1181 and 1182:
1.3.3 Median and Selection 1.3.3 Me
Page 1183 and 1184:
1.3.1 Sorting 1.3.1 Sorting INPUT O
Page 1185 and 1186:
Plugins for use with the CDROM Plug
Page 1187 and 1188:
Implementation Challenges Next: Dat
Page 1189 and 1190:
Implementation Challenges Next: Gra
Page 1191 and 1192:
Implementation Challenges Next: Int
Page 1193 and 1194:
Caveats Next: Data Structures Up: A
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1.1.1 Dictionaries ● Priority Que
Page 1197 and 1198:
1.1.4 Graph Data Structures ● Gra
Page 1199 and 1200:
1.1.5 Set Data Structures ● Gener
Page 1201 and 1202:
1.2.1 Solving Linear Equations ●
Page 1203 and 1204:
1.2.2 Bandwidth Reduction ● Topol
Page 1205 and 1206:
1.2.4 Determinants and Permanents
Page 1207 and 1208:
1.2.8 Factoring and Primality Testi
Page 1209 and 1210:
1.2.9 Arbitrary Precision Arithmeti
Page 1211 and 1212:
1.2.10 Knapsack Problem ● Linear
Page 1213 and 1214:
1.3.2 Searching ● Sorting Go to t
Page 1215 and 1216:
1.3.4 Generating Permutations ● C
Page 1217 and 1218:
1.3.5 Generating Subsets ● Genera
Page 1219 and 1220:
1.3.6 Generating Partitions ● Gen
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1.3.8 Calendrical Calculations Go t
Page 1223 and 1224:
1.3.9 Job Scheduling ● Feedback E
Page 1225 and 1226:
1.4.2 Topological Sorting Related P
Page 1227 and 1228:
1.4.8 Edge and Vertex Connectivity
Page 1229 and 1230:
1.4.10 Drawing Graphs Nicely ● Pl
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1.4.11 Drawing Trees ● Planarity
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1.4.12 Planarity Detection and Embe
Page 1235 and 1236:
1.5.2 Independent Set ● Vertex Co
Page 1237 and 1238:
1.5.3 Vertex Cover ● Independent
Page 1239 and 1240:
1.5.4 Traveling Salesman Problem
Page 1241 and 1242:
1.5.6 Graph Partition ● Network F
Page 1243 and 1244:
1.5.7 Vertex Coloring Related Probl
Page 1245 and 1246:
1.5.11 Feedback Edge/Vertex Set Go
Page 1247 and 1248:
1.6.1 Robust Geometric Primitives G
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1.6.6 Range Search ● Kd-Trees ●
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1.6.8 Intersection Detection ● Ro
Page 1253 and 1254:
1.6.16 Minkowski Sum Go to the corr
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1.7.1 Set Cover ● Set Packing ●
Page 1257 and 1258:
1.7.2 Set Packing Go to the corresp
Page 1259 and 1260:
1.7.3 String Matching ● Approxima
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1.7.4 Approximate String Matching
Page 1263 and 1264:
1.7.5 Text Compression Go to the co
Page 1265 and 1266:
1.7.6 Cryptography ● Text Compres
Page 1267 and 1268:
1.7.7 Finite State Machine Minimiza
Page 1269 and 1270:
1.7.8 Longest Common Substring ●
Page 1271 and 1272:
1.7.9 Shortest Common Superstring G
Page 1273 and 1274:
Handbook of Algorithms and Data Str
Page 1275 and 1276:
Moret and Shapiro's Algorithms P to
Page 1277 and 1278:
Index B Up: Index - All Index: B ba
Page 1279 and 1280:
Index C Up: Index - All Index: C ch
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Index E Up: Index - All Index: E ed
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Index G Up: Index - All Index: G ga
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Index I Up: Index - All Index: I in
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Index L Up: Index - All Index: L li
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Index N Up: Index - All Index: N ne
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Index P Up: Index - All Index: P pa
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Index R Up: Index - All Index: R RA
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Index S successor supercomputer , s
Page 1297 and 1298:
Index U Up: Index - All Index: U un
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Index W Up: Index - All Index: W wo
Page 1301 and 1302:
Index (complete) bin packing bipart
Page 1303 and 1304:
Index (complete) Fourier transform
Page 1305 and 1306:
Index (complete) parenthesization p
Page 1307 and 1308:
Index (complete) symmetry, exploiti
Page 1309 and 1310:
Ranger - Nearest Neighbor Search in
Page 1311 and 1312:
DIMACS Implementation Challenges Pe
Page 1313 and 1314:
Stony Brook Project Implementations
Page 1315 and 1316:
Clarkson's higher dimensional conve
Page 1317 and 1318:
file:///E|/WEBSITE/BIBLIO/TESTDATA/
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SimPack/Sim++ Simulation Toolkit Si
Page 1449 and 1450:
Fire-Engine and Spare-Parts String
Page 1451 and 1452:
Geolab -- Computational Geometry Sy
Page 1453 and 1454:
Calendrical Calculations Calendrica
Page 1455 and 1456:
David Eppstein's Knuth-Morris-Pratt
Page 1457 and 1458:
Mike Trick's Graph Coloring Resourc
Page 1459 and 1460:
Frank Ruskey's Combinatorial Genera
Page 1461 and 1462:
Arrange - maintainance of arrangeme
Page 1463 and 1464:
LP_SOLVE: Linear Programming Code L
Page 1465 and 1466:
PARI - Package for Number Theory Se
Page 1467 and 1468:
TSP solvers TSP solvers tsp-solve i
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PHYLIP -- inferring phylogenic tree
Page 1471 and 1472:
Skeletonization Software (2-D) Skel
Page 1473 and 1474:
agrep - Approximate General Regular
Page 1475 and 1476:
CAP -- Contig Assembly Program CAP
Page 1477 and 1478:
NAUTY -- Graph Isomorphism NAUTY --
Page 1479 and 1480:
BIPM -- Bipartite Matching Codes BI
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LAPACK and LINPACK -- Linear Algebr
Page 1483 and 1484:
User Comments User Comments Archive
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The Algorithm Design Manual Most pr
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The Algorithm Design Manual 5.6 War
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