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

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Graph Algorithms Next: The Friendship Graph Up: Techniques Previous: Implementation Challenges Graph Algorithms A graph G=(V,E) consists of a set of vertices V together with a set E of vertex pairs or edges. Graphs are important because they can be used to represent essentially any relationship. For example, graphs can model a network of roads, with cities as vertices and roads between cities as edges, as shown in Figure . Electronic circuits can also be modeled as graphs, with junctions as vertices and components as edges. Figure: Modeling road networks and electronic circuits as graphs The key to understanding many algorithmic problems is to think of them in terms of graphs. Graph theory provides a language for talking about the properties of graphs, and it is amazing how often messy applied problems have a simple description and solution in terms of classical graph properties. Designing truly novel graph algorithms is a very difficult task. The key to using graph algorithms effectively in applications lies in correctly modeling your problem as a standard graph property, so you can take advantage of existing algorithms. Becoming familiar with many different graph algorithmic problems is more important than understanding the details of particular graph algorithms, particularly since Part II of this book can point you to an implementation as soon as you know the name of your problem. In this chapter, we will present basic data structures and traversal operations for graphs, which will enable you to cobble together solutions to rudimentary graph problems. We will also describe more sophisticated algorithms for problems like shortest paths and minimum spanning trees in some detail. But we stress the primary importance of correctly modeling your problem. Time spent browsing through the catalog now will leave you better informed of your options when a real job arises. file:///E|/BOOK/BOOK2/NODE59.HTM (1 of 3) [19/1/2003 1:27:44]
Graph Algorithms The take-home lessons of this chapter include: ● Graphs can be used to model a wide variety of structures and relationships. ● Properly formulated, most applications of graphs can be reduced to standard graph properties and using well-known algorithms. These include minimum spanning trees, shortest paths, and several problems presented in the catalog. ● Breadth-first and depth-first search provide mechanisms to visit each edge and vertex of the graph. They prove the basis of most simple, efficient graph algorithms. ● The Friendship Graph ● Data Structures for Graphs ● War Story: Getting the Graph ● Traversing a Graph ❍ Breadth-First Search ❍ Depth-First Search ● Applications of Graph Traversal ❍ Connected Components ❍ Tree and Cycle Detection ❍ Two-Coloring Graphs ❍ Topological Sorting ❍ Articulation Vertices ● Modeling Graph Problems ● Minimum Spanning Trees ❍ Prim's Algorithm ❍ Kruskal's Algorithm ● Shortest Paths ❍ Dijkstra's Algorithm ❍ All-Pairs Shortest Path ● War Story: Nothing but Nets ● War Story: Dialing for Documents ● Exercises file:///E|/BOOK/BOOK2/NODE59.HTM (2 of 3) [19/1/2003 1:27:44]
Page 1 and 2: The Algorithm Design Manual Next: P
Page 3 and 4: Preface Next: Acknowledgments Up: T
Page 5 and 6: Preface one stressing design over a
Page 7 and 8: Acknowledgments Mon Jun 2 23:33:50
Page 9 and 10: Contents Next: Techniques Up: The A
Page 11 and 12: Contents ■ All-Pairs Shortest Pat
Page 13 and 14: Contents ■ Graph Problems: Polyno
Page 15 and 16: Contents ● About this document ..
Page 17 and 18: The Algorithm Design Manual The Alg
Page 19 and 20: Lecture Notes -- Analysis of Algori
Page 21 and 22: Lecture Notes -- Analysis of Algori
Page 23 and 24: The Stony Brook Algorithm Repositor
Page 25 and 26: Techniques Next: Introduction to Al
Page 27 and 28: Techniques Algorithms Mon Jun 2 23:
Page 29 and 30: Introduction to Algorithms ● Reas
Page 31 and 32: Data Structures and Sorting divide-
Page 33: Breaking Problems Down ● Dynamic
Page 37 and 38: Combinatorial Search and Heuristic
Page 39 and 40: Intractable Problems and Approximat
Page 41 and 42: How to Design Algorithms Next: Reso
Page 43 and 44: How to Design Algorithms with a cou
Page 45 and 46: How to Design Algorithms Next: Reso
Page 47 and 48: A Catalog of Algorithmic Problems N
Page 49 and 50: A Catalog of Algorithmic Problems
Page 51 and 52: Algorithmic Resources Next: Softwar
Page 53 and 54: References L. Adleman. Algorithmic
Page 55 and 56: References AS89 Ata83 Ata84 problem
Page 57 and 58: References BJL 91 A. Blum, T. Jiang
Page 59 and 60: References BS81 BS86 BS93 BS96 BS97
Page 61 and 62: References J. M. Chambers. Partial
Page 63 and 64: References CT80 CT92 1971. G. Carpa
Page 65 and 66: References K. Daniels and V. Milenk
Page 67 and 68: References (FOCS), pages 60-69, 199
Page 69 and 70: References FM71 M. Fischer and A. M
Page 71 and 72: References History of Computing, 7:
Page 73 and 74: References N. Gibbs, W. Poole, and
Page 75 and 76: References Hof82 Hof89 Hol75 C. M.
Page 77 and 78: References IK75 Ita78 O. Ibarra and
Page 79 and 80: References Kir83 D. Kirkpatrick. Ef
Page 81 and 82: References object in 2-dimensional
Page 83 and 84: References LT79 LT80 8:99-118, 1995
Page 85 and 86:
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
Page 105 and 106:
Correctness NearestNeighborTSP(P) P
Page 107 and 108:
Correctness Figure: A bad example f
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Efficiency Next: Expressing Algorit
Page 111 and 112:
Keeping Score Next: The RAM Model o
Page 113 and 114:
The RAM Model of Computation substa
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Best, Worst, and Average-Case Compl
Page 117 and 118:
The Big Oh Notation Figure: Illustr
Page 119 and 120:
Logarithms Next: Modeling the Probl
Page 121 and 122:
Logarithms justified in ignoring th
Page 123 and 124:
Modeling the Problem Figure: Modeli
Page 125 and 126:
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
Page 131 and 132:
War Story: Psychic Modeling Next: E
Page 133 and 134:
Exercises (b) If I prove that an al
Page 135 and 136:
Fundamental Data Types Next: Contai
Page 137 and 138:
Containers Next: Dictionaries Up: F
Page 139 and 140:
Dictionaries Next: Binary Search Tr
Page 141 and 142:
Binary Search Trees BinaryTreeQuery
Page 143 and 144:
Priority Queues Next: Specialized D
Page 145 and 146:
Specialized Data Structures Next: S
Page 147 and 148:
Sorting Next: Applications of Sorti
Page 149 and 150:
Applications of Sorting Figure: Con
Page 151 and 152:
Data Structures Next: Incremental I
Page 153 and 154:
Incremental Insertion Next: Divide
Page 155 and 156:
Randomization Next: Bucketing Techn
Page 157 and 158:
Randomization Next: Bucketing Techn
Page 159 and 160:
Bucketing Techniques Algorithms Mon
Page 161 and 162:
War Story: Stripping Triangulations
Page 163 and 164:
War Story: Stripping Triangulations
Page 165 and 166:
War Story: Mystery of the Pyramids
Page 167 and 168:
War Story: Mystery of the Pyramids
Page 169 and 170:
War Story: String 'em Up We were co
Page 171 and 172:
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.
Page 177 and 178:
Dynamic Programming Next: Fibonacci
Page 179 and 180:
Fibonacci numbers Next: The Partiti
Page 181 and 182:
Fibonacci numbers Next: The Partiti
Page 183 and 184:
The Partition Problem . What is the
Page 185 and 186:
The Partition Problem Figure: Dynam
Page 187 and 188:
Approximate String Matching Next: L
Page 189 and 190:
Approximate String Matching The val
Page 191 and 192:
Longest Increasing Sequence Will th
Page 193 and 194:
Minimum Weight Triangulation Next:
Page 195 and 196:
Limitations of Dynamic Programming
Page 197 and 198:
War Story: Evolution of the Lobster
Page 199 and 200:
War Story: Evolution of the Lobster
Page 201 and 202:
War Story: What's Past is Prolog Ne
Page 203 and 204:
War Story: What's Past is Prolog th
Page 205 and 206:
War Story: Text Compression for Bar
Page 207 and 208:
War Story: Text Compression for Bar
Page 209 and 210:
Divide and Conquer Next: Fast Expon
Page 211 and 212:
Fast Exponentiation Next: Binary Se
Page 213 and 214:
Binary Search Next: Square and Othe
Page 215 and 216:
Page 217 and 218:
Exercises whose denominations are ,
Page 219 and 220:
The Friendship Graph Next: Data Str
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The Friendship Graph friendship gra
Page 223 and 224:
Data Structures for Graphs linked t
Page 225 and 226:
War Story: Getting the Graph ``Well
Page 227 and 228:
Traversing a Graph Next: Breadth-Fi
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Breadth-First Search Next: Depth-Fi
Page 231 and 232:
Depth-First Search Next: Applicatio
Page 233 and 234:
Depth-First Search Next: Applicatio
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Connected Components Next: Tree and
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Two-Coloring Graphs Next: Topologic
Page 239 and 240:
Topological Sorting Next: Articulat
Page 241 and 242:
Modeling Graph Problems Next: Minim
Page 243 and 244:
Modeling Graph Problems good line s
Page 245 and 246:
Minimum Spanning Trees ● Prim's A
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Prim's Algorithm inserted edge (x,y
Page 249 and 250:
Kruskal's Algorithm a tree of weigh
Page 251 and 252:
Dijkstra's Algorithm Next: All-Pair
Page 253 and 254:
All-Pairs Shortest Path Next: War S
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War Story: Nothing but Nets Next: W
Page 257 and 258:
War Story: Nothing but Nets ``You a
Page 259 and 260:
War Story: Dialing for Documents Ne
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War Story: Dialing for Documents If
Page 263 and 264:
War Story: Dialing for Documents CO
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Page 267 and 268:
Exercises Prove the statement or gi
Page 269 and 270:
Backtracking report it. kth element
Page 271 and 272:
Constructing All Subsets Next: Cons
Page 273 and 274:
Constructing All Paths in a Graph N
Page 275 and 276:
Search Pruning Next: Bandwidth Mini
Page 277 and 278:
Bandwidth Minimization immediately
Page 279 and 280:
War Story: Covering Chessboards Nex
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War Story: Covering Chessboards att
Page 283 and 284:
Heuristic Methods Mon Jun 2 23:33:5
Page 285 and 286:
Simulated Annealing Return S then u
Page 287 and 288:
Traveling Salesman Problem Next: Ma
Page 289 and 290:
Independent Set Next: Circuit Board
Page 291 and 292:
Neural Networks Next: Genetic Algor
Page 293 and 294:
Genetic Algorithms Next: War Story:
Page 295 and 296:
War Story: Annealing Arrays Next: P
Page 297 and 298:
War Story: Annealing Arrays optimal
Page 299 and 300:
Parallel Algorithms Next: War Story
Page 301 and 302:
War Story: Going Nowhere Fast Next:
Page 303 and 304:
Page 305 and 306:
Problems and Reductions Next: Simpl
Page 307 and 308:
Simple Reductions Next: Hamiltonian
Page 309 and 310:
Hamiltonian Cycles Next: Independen
Page 311 and 312:
Independent Set and Vertex Cover pr
Page 313 and 314:
Clique and Independent Set These la
Page 315 and 316:
Satisfiability Mon Jun 2 23:33:50 E
Page 317 and 318:
The Theory of NP-Completeness Next:
Page 319 and 320:
3-Satisfiability where for , , , an
Page 321 and 322:
Integer Programming Next: Vertex Co
Page 323 and 324:
Integer Programming possible IP ins
Page 325 and 326:
Vertex Cover reduction for the 3-SA
Page 327 and 328:
Other NP-Complete Problems hard. Th
Page 329 and 330:
The Art of Proving Hardness easiest
Page 331 and 332:
War Story: Hard Against the Clock N
Page 333 and 334:
War Story: Hard Against the Clock I
Page 335 and 336:
Approximation Algorithms Next: Appr
Page 337 and 338:
Approximating Vertex Cover Next: Th
Page 339 and 340:
The Euclidean Traveling Salesman Ne
Page 341 and 342:
The Euclidean Traveling Salesman Ne
Page 343 and 344:
Exercises 1. Prove that the low deg
Page 345 and 346:
Data Structures Next: Dictionaries
Page 347 and 348:
Dictionaries Next: Priority Queues
Page 349 and 350:
Dictionaries use a function that ma
Page 351 and 352:
Dictionaries Implementation-oriente
Page 353 and 354:
Priority Queues ● Besides access
Page 355 and 356:
Priority Queues Fibonacci heaps [FT
Page 357 and 358:
Suffix Trees and Arrays Figure: A t
Page 359 and 360:
Suffix Trees and Arrays [GBY91]. Se
Page 361 and 362:
Graph Data Structures algorithms).
Page 363 and 364:
Graph Data Structures including the
Page 365 and 366:
Set Data Structures Next: Kd-Trees
Page 367 and 368:
Set Data Structures parent pointers
Page 369 and 370:
Kd-Trees Next: Numerical Problems U
Page 371 and 372:
Kd-Trees about p. Say we are lookin
Page 373 and 374:
Numerical Problems Next: Solving Li
Page 375 and 376:
Numerical Problems Mon Jun 2 23:33:
Page 377 and 378:
Solving Linear Equations algorithm
Page 379 and 380:
Solving Linear Equations Matrix inv
Page 381 and 382:
Bandwidth Reduction images near eac
Page 383 and 384:
Matrix Multiplication Next: Determi
Page 385 and 386:
Matrix Multiplication The linear al
Page 387 and 388:
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 and 442:
Generating Subsets look right when
Page 443 and 444:
Generating Subsets above for detail
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
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 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|/
Page 839 and 840:
Binary Search in Action file:///E|/
Page 841 and 842:
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 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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