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

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Generating Subsets Generation problems for two closely related problems arise often in practice: ● k-subsets - Instead of constructing all subsets, we may only be interested in the subsets containing exactly k elements. There are particularly for small values of k. such subsets, which is substantially less than , The best way to construct all k-subsets is in lexicographic order. The ranking function is based on the observation that there are k-subsets whose smallest element is f. Using this, it is possible to determine the smallest element in the mth k-subset of n items. We then proceed recursively for subsequent elements of the subset. See the implementations below for details. ● Strings - Generating all subsets is equivalent to generating all strings of true and false. To generate all or random strings on alphabets of size , the same basic techniques apply, except there will be strings in total. Implementations: Nijenhuis and Wilf [NW78] provide efficient Fortran implementations of algorithms to construct random subsets and to sequence subsets in Gray code and lexicographic order. They also provide routines to construct random k-subsets and sequence them in lexicographic order. See Section for details on ftp-ing these programs. Algorithm 515 [BL77] of the Collected Algorithms of the ACM is another Fortran implementation of lexicographic k-subsets, available from Netlib (see Section ). An exciting WWW site developed by Frank Ruskey of the University of Victoria contains a wealth of material on generating combinatorial objects of different types, including permutations, subsets, partitions, and certain graphs. Specifically, it provides an interactive interface that lets you specify which type of objects you would like to construct and then returns the objects to you. Check this out at http://sue.csc.uvic.ca/ cos/. Combinatorica [Ski90] provides Mathematica implementations of algorithms to construct random subsets and to sequence subsets in Gray code, binary, and lexicographic order. They also provide routines to construct random k-subsets and strings, and sequence them lexicographically. See Section for further information on Combinatorica. Notes: The primary expositions on subset generation include [NW78, RND77, Rus97]. Wilf [Wil89] provides an update of [NW78], including a thorough discussion of modern Gray code generation problems. Gray codes were first developed [Gra53] to transmit digital information in a robust manner over an analog channel. By assigning the code words in Gray code order, the ith word differs only slightly from the (i+1)st, so minor fluctuations in analog signal strength corrupts only a few bits. Gray codes have a particularly nice correspondence to Hamiltonian cycles on the hypercube. See any of the references file:///E|/BOOK/BOOK4/NODE152.HTM (3 of 4) [19/1/2003 1:30:44]
Generating Subsets above for details. An exposition on the more general problem of constructing Gray codes for k items (instead of subsets) appears in [Man89]. The popular puzzle Spinout, manufactured by Binary Arts Corporation, can be solved using Gray codes. Related Problems: Generating permutations (see page ), generating partitions (see page ). Next: Generating Partitions Up: Combinatorial Problems Previous: Generating Permutations Algorithms Mon Jun 2 23:33:50 EDT 1997 file:///E|/BOOK/BOOK4/NODE152.HTM (4 of 4) [19/1/2003 1:30:44]
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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:
Page 29 and 30:
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:
Page 103 and 104:
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
Page 127 and 128:
War Story: Psychic Modeling Next: E
Page 129 and 130:
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
Page 145 and 146:
Specialized Data Structures Next: S
Page 147 and 148:
Sorting Next: Applications of Sorti
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Applications of Sorting Figure: Con
Page 151 and 152:
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
Page 173 and 174:
Exercises Next: Implementation Chal
Page 175 and 176:
Exercises used to select the pivot.
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Dynamic Programming Next: Fibonacci
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Fibonacci numbers Next: The Partiti
Page 181 and 182:
Fibonacci numbers Next: The Partiti
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The Partition Problem . What is the
Page 185 and 186:
The Partition Problem Figure: Dynam
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Approximate String Matching Next: L
Page 189 and 190:
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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Page 217 and 218:
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
Page 389 and 390:
Determinants and Permanents exposit
Page 391 and 392: Constrained and Unconstrained Optim
Page 393 and 394: Constrained and Unconstrained Optim
Page 395 and 396: Linear Programming variable assignm
Page 397 and 398: Linear Programming The book [MW93]
Page 399 and 400: Random Number Generation Next: Fact
Page 401 and 402: Random Number Generation is largely
Page 403 and 404: Random Number Generation Related Pr
Page 405 and 406: Factoring and Primality Testing The
Page 407 and 408: Factoring and Primality Testing Alg
Page 409 and 410: Arbitrary-Precision Arithmetic If y
Page 411 and 412: Arbitrary-Precision Arithmetic PARI
Page 413 and 414: Knapsack Problem Next: Discrete Fou
Page 415 and 416: Knapsack Problem is a subset of S'
Page 417 and 418: Discrete Fourier Transform Next: Co
Page 419 and 420: Discrete Fourier Transform an algor
Page 421 and 422: Combinatorial Problems Next: Sortin
Page 423 and 424: Sorting Next: Searching Up: Combina
Page 425 and 426: Sorting The simplest approach to ex
Page 427 and 428: Sorting operations, implying an sor
Page 429 and 430: Searching large performance improve
Page 431 and 432: Searching Notes: Mehlhorn and Tsaka
Page 433 and 434: Median and Selection followed by fi
Page 435 and 436: Generating Permutations Next: Gener
Page 437 and 438: Generating Permutations The rank/un
Page 439 and 440: Generating Permutations generating
Page 441: Generating Subsets look right when
Page 445 and 446: Generating Partitions Although the
Page 447 and 448: Generating Partitions Two related c
Page 449 and 450: Generating Graphs generate: ● Do
Page 451 and 452: Generating Graphs Combinatorica [Sk
Page 453 and 454: Calendrical Calculations Next: Job
Page 455 and 456: Calendrical Calculations Gregorian,
Page 457 and 458: 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
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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 and 510:
Planarity Detection and Embedding N
Page 511 and 512:
Planarity Detection and Embedding p
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
Page 563 and 564:
Convex Hull http://www.cs.att.com/n
Page 565 and 566:
Triangulation Next: Voronoi Diagram
Page 567 and 568:
Triangulation GEOMPACK is a suite o
Page 569 and 570:
Voronoi Diagrams Next: Nearest Neig
Page 571 and 572:
Voronoi Diagrams McDonald's, the ti
Page 573 and 574:
Nearest Neighbor Search Next: Range
Page 575 and 576:
Nearest Neighbor Search Implementat
Page 577 and 578:
Range Search Next: Point Location U
Page 579 and 580:
Range Search subdivisions in C++. I
Page 581 and 582:
Point Location the n edges for inte
Page 583 and 584:
Point Location More recently, there
Page 585 and 586:
Intersection Detection ● Do you w
Page 587 and 588:
Intersection Detection Implementati
Page 589 and 590:
Bin Packing Next: Medial-Axis Trans
Page 591 and 592:
Bin Packing approach for general sh
Page 593 and 594:
Medial-Axis Transformation Next: Po
Page 595 and 596:
Medial-Axis Transformation Implemen
Page 597 and 598:
Polygon Partitioning number of piec
Page 599 and 600:
Simplifying Polygons Next: Shape Si
Page 601 and 602:
Simplifying Polygons vertices and o
Page 603 and 604:
Shape Similarity Next: Motion Plann
Page 605 and 606:
Shape Similarity or how close it is
Page 607 and 608:
Motion Planning There is a wide ran
Page 609 and 610:
Motion Planning often arise in the
Page 611 and 612:
Maintaining Line Arrangements Think
Page 613 and 614:
Maintaining Line Arrangements Next:
Page 615 and 616:
Minkowski Sum where x+y is the vect
Page 617 and 618:
Set and String Problems Next: Set C
Page 619 and 620:
Set Cover Next: Set Packing Up: Set
Page 621 and 622:
Set Cover Figure: Hitting set is du
Page 623 and 624:
Set Packing Next: String Matching U
Page 625 and 626:
Set Packing Notes: An excellent exp
Page 627 and 628:
String Matching shouldn't try. Furt
Page 629 and 630:
String Matching and texts, I recomm
Page 631 and 632:
Approximate String Matching This sa
Page 633 and 634:
Approximate String Matching http://
Page 635 and 636:
Text Compression Next: Cryptography
Page 637 and 638:
Text Compression code string. ASCII
Page 639 and 640:
Cryptography Next: Finite State Mac
Page 641 and 642:
Cryptography ● How can I validate
Page 643 and 644:
Cryptography MD5 [Riv92] is the sec
Page 645 and 646:
Finite State Machine Minimization F
Page 647 and 648:
Finite State Machine Minimization S
Page 649 and 650:
Longest Common Substring than edit
Page 651 and 652:
Longest Common Substring include [A
Page 653 and 654:
Shortest Common Superstring Finding
Page 655 and 656:
Software systems Next: LEDA Up: Alg
Page 657 and 658:
LEDA Next: Netlib Up: Software syst
Page 659 and 660:
Netlib Algorithms Mon Jun 2 23:33:5
Page 661 and 662:
The Stanford GraphBase Next: Combin
Page 663 and 664:
Algorithm Animations with XTango Ne
Page 665 and 666:
Programs from Books Next: Discrete
Page 667 and 668:
Handbook of Data Structures and Alg
Page 669 and 670:
Algorithms from P to NP Next: Compu
Page 671 and 672:
Algorithms in C++ Next: Data Source
Page 673 and 674:
Textbooks Next: On-Line Resources U
Page 675 and 676:
On-Line Resources Next: Literature
Page 677 and 678:
People Next: Software Up: On-Line R
Page 679 and 680:
Professional Consulting Services Ne
Page 681 and 682:
Index A Up: Index - All Index: A ab
Page 683 and 684:
Index A artists steal ASA ASCII asp
Page 685 and 686:
Index B binary representation - sub
Page 687 and 688:
Index C Up: Index - All Index: C C+
Page 689 and 690:
Index C clustering , , co-NP coding
Page 691 and 692:
Index C consulting services , conta
Page 693 and 694:
Index D Up: Index - All Index: D DA
Page 695 and 696:
Index D Dictionaries dictionaries -
Page 697 and 698:
Index D dynamic programming - appli
Page 699 and 700:
Index E empirical results - heurist
Page 701 and 702:
Index F Up: Index - All Index: F fa
Page 703 and 704:
Index F frequency domain friend-or-
Page 705 and 706:
Index G geometric shortest path , g
Page 707 and 708:
Index H Up: Index - All Index: H ha
Page 709 and 710:
Index H Algorithms Tue Jun 3 11:59:
Page 711 and 712:
Index I independent set - alternate
Page 713 and 714:
Index J Up: Index - All Index: J ji
Page 715 and 716:
Index K Algorithms Tue Jun 3 11:59:
Page 717 and 718:
Index L linear congruential generat
Page 719 and 720:
Index M Up: Index - All Index: M ma
Page 721 and 722:
Index M mindset minima minimax sear
Page 723 and 724:
Index N Up: Index - All Index: N na
Page 725 and 726:
Index N numerical analysis numerica
Page 727 and 728:
Index O overlap graph overpasses -
Page 729 and 730:
Index P , , , , , , , , , , passwor
Page 731 and 732:
Index P polygons polygon triangulat
Page 733 and 734:
Index Q Up: Index - All Index: Q Qh
Page 735 and 736:
Index R ranking combinatorial objec
Page 737 and 738:
Index S Up: Index - All Index: S s-
Page 739 and 740:
Index S Shape Similarity shape simp
Page 741 and 742:
Index S solar year Solving Linear E
Page 743 and 744:
Index S straight-line graph drawing
Page 745 and 746:
Index T Up: Index - All Index: T ta
Page 747 and 748:
Index T trees - matching trees - pa
Page 749 and 750:
Index V Up: Index - All Index: V va
Page 751 and 752:
Index W Up: Index - All Index: W wa
Page 753 and 754:
Index Y Up: Index - All Index: Y Yo
Page 755 and 756:
Index (complete) Up: Index - All In
Page 757 and 758:
Index (complete) arm, robot around
Page 759 and 760:
Index (complete) binary search tree
Page 761 and 762:
Index (complete) center vertex, , C
Page 763 and 764:
Index (complete) compaction compari
Page 765 and 766:
Index (complete) counting paths, co
Page 767 and 768:
Index (complete) deletion from bina
Page 769 and 770:
Index (complete) dominance ordering
Page 771 and 772:
Index (complete) English to French
Page 773 and 774:
Index (complete) file directory tre
Page 775 and 776:
Index (complete) geom.bib, geometri
Page 777 and 778:
Index (complete) Hamiltonian Cycle
Page 779 and 780:
Index (complete) implementation cha
Page 781 and 782:
Index (complete) job-shop schedulin
Page 783 and 784:
Index (complete) linear programming
Page 785 and 786:
Index (complete) , , , , , , , math
Page 787 and 788:
Index (complete) modular arithmetic
Page 789 and 790:
Index (complete) normal distributio
Page 791 and 792:
Index (complete) parallel algorithm
Page 793 and 794:
Index (complete) planar subdivision
Page 795 and 796:
Index (complete) proof of correctne
Page 797 and 798:
Index (complete) regular expression
Page 799 and 800:
Index (complete) self-organizing tr
Page 801 and 802:
Index (complete) sine functions sin
Page 803 and 804:
Index (complete) spring embedding h
Page 805 and 806:
Index (complete) Symbol Technologie
Page 807 and 808:
Index (complete) trial division Tri
Page 809 and 810:
Index (complete) VLSI circuit layou
Page 811 and 812:
1.4.4 Shortest Path 1.4.4 Shortest
Page 813 and 814:
1.2.5 Constrained and Unconstrained
Page 815 and 816:
1.6.4 Voronoi Diagrams 1.6.4 Vorono
Page 817 and 818:
1.4.7 Eulerian Cycle / Chinese Post
Page 819 and 820:
Online Bibliographies Online Biblio
Page 821 and 822:
About the Book -- The Algorithm Des
Page 823 and 824:
Copyright and Disclaimers Copyright
Page 825 and 826:
CD-ROM Installation Installation an
Page 827 and 828:
CD-ROM Installation install a sound
Page 829 and 830:
Thanks! Frank Ruscica file:///E|/WE
Page 831 and 832:
Thanks! Zhong Li Thanks also to Fil
Page 833 and 834:
CD-ROM Installation To use the CD-R
Page 835 and 836:
Binary Search in Action Binary Sear
Page 837 and 838:
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
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1.1.6 Kd-Trees ● Point Location
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1.1.3 Suffix Trees and Arrays Send
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1.5.1 Clique ● Vertex Cover Go to
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1.6.2 Convex Hull Related Problems
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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
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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
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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
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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
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Genocop -- Optimization via Genetic
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1.2.6 Linear Programming ● Knapsa
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1.2.7 Random Number Generation ●
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1.3.10 Satisfiability ● Constrain
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Qhull - higher dimensional convex h
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1.6.5 Nearest Neighbor Search 1.6.5
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1.6.7 Point Location 1.6.7 Point Lo
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1.6.10 Medial-Axis Transformation 1
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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
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1.4.6 Matching 1.4.6 Matching INPUT
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A compendium of NP optimization pro
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1.6.9 Bin Packing 1.6.9 Bin Packing
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1.6.12 Simplifying Polygons 1.6.12
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1.6.13 Shape Similarity 1.6.13 Shap
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1.6.11 Polygon Partitioning 1.6.11
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1.4.3 Minimum Spanning Tree 1.4.3 M
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1.6.15 Maintaining Line Arrangement
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1.3.7 Generating Graphs 1.3.7 Gener
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1.2.11 Discrete Fourier Transform 1
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1.5.8 Edge Coloring 1.5.8 Edge Colo
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1.3.3 Median and Selection 1.3.3 Me
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1.3.1 Sorting 1.3.1 Sorting INPUT O
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Plugins for use with the CDROM Plug
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Implementation Challenges Next: Dat
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Implementation Challenges Next: Gra
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Implementation Challenges Next: Int
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Caveats Next: Data Structures Up: A
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1.1.1 Dictionaries ● Priority Que
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1.1.4 Graph Data Structures ● Gra
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1.1.5 Set Data Structures ● Gener
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1.2.1 Solving Linear Equations ●
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1.2.2 Bandwidth Reduction ● Topol
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1.2.4 Determinants and Permanents
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1.2.8 Factoring and Primality Testi
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1.2.9 Arbitrary Precision Arithmeti
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1.2.10 Knapsack Problem ● Linear
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1.3.2 Searching ● Sorting Go to t
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1.3.4 Generating Permutations ● C
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1.3.5 Generating Subsets ● Genera
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1.3.6 Generating Partitions ● Gen
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1.3.8 Calendrical Calculations Go t
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1.3.9 Job Scheduling ● Feedback E
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1.4.2 Topological Sorting Related P
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1.4.8 Edge and Vertex Connectivity
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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
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1.5.2 Independent Set ● Vertex Co
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1.5.3 Vertex Cover ● Independent
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1.5.4 Traveling Salesman Problem
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1.5.6 Graph Partition ● Network F
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1.5.7 Vertex Coloring Related Probl
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1.5.11 Feedback Edge/Vertex Set Go
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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
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1.6.16 Minkowski Sum Go to the corr
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1.7.1 Set Cover ● Set Packing ●
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1.7.2 Set Packing Go to the corresp
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1.7.3 String Matching ● Approxima
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1.7.4 Approximate String Matching
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1.7.5 Text Compression Go to the co
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1.7.6 Cryptography ● Text Compres
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1.7.7 Finite State Machine Minimiza
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1.7.8 Longest Common Substring ●
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1.7.9 Shortest Common Superstring G
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Handbook of Algorithms and Data Str
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Moret and Shapiro's Algorithms P to
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Index B Up: Index - All Index: B ba
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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
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Index U Up: Index - All Index: U un
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Index W Up: Index - All Index: W wo
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Index (complete) bin packing bipart
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Index (complete) Fourier transform
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Index (complete) parenthesization p
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Index (complete) symmetry, exploiti
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Ranger - Nearest Neighbor Search in
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DIMACS Implementation Challenges Pe
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Stony Brook Project Implementations
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Clarkson's higher dimensional conve
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file:///E|/WEBSITE/BIBLIO/TESTDATA/
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SimPack/Sim++ Simulation Toolkit Si
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Fire-Engine and Spare-Parts String
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Geolab -- Computational Geometry Sy
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Calendrical Calculations Calendrica
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David Eppstein's Knuth-Morris-Pratt
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Mike Trick's Graph Coloring Resourc
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Frank Ruskey's Combinatorial Genera
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Arrange - maintainance of arrangeme
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LP_SOLVE: Linear Programming Code L
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PARI - Package for Number Theory Se
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TSP solvers TSP solvers tsp-solve i
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PHYLIP -- inferring phylogenic tree
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Skeletonization Software (2-D) Skel
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agrep - Approximate General Regular
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CAP -- Contig Assembly Program CAP
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NAUTY -- Graph Isomorphism NAUTY --
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BIPM -- Bipartite Matching Codes BI
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LAPACK and LINPACK -- Linear Algebr
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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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