Combinatorial Algorithms (eBook)

Enlarged Second Edition

T. C. Hu, M. T. Shing (Autoren)

eBook Download: EPUB

2012 | 2., Second Edition, Enlarged
368 Seiten
Dover Publications (Verlag)
9780486152943 (ISBN)

Infos

This updated edition presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. Includes 153 black-and-white illustrations and 23 tables.

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Newly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9 shows how to mix known algorithms and create new ones, while Chapter 10 presents the "e;Chop-Sticks"e; algorithm, used to obtain all minimum cuts in an undirected network without applying traditional maximum flow techniques. This algorithm has led to the new mathematical specialty of network algebra. The text assumes no background in linear programming or advanced data structure, and most of the material is suitable for undergraduates. 153 black-and-white illus. 23 tables. Exercises, with answers at the ends of chapters.

Inhalt

Chapter 1. Shortest Paths 1.1 Graph terminology 1.2 Shortest path 1.3 Multiterminal shortest paths 1.4 Decomposition algorithm 1.5 Acyclic network 1.6 Shortest paths in a general network 1.7 Minimum spanning tree 1.8 Breadth-first-search and depth-first-searchChapter 2. Maximum flows 2.1 Maximum flow 2.2 Algorithms for max flows 2.2.1 Ford and Fulkerson 2.2.2 Karzanov's algorithm 2.2.3 MPM algorithms 2.2.4 Analysis of algorithms 2.3 Multi-terminal maximum flows 2.3.1 Realization 2.3.2 Analysis 2.3.3 Synthesis 2.3.4 Multi-commodity flows 2.4 Minimum cost flows 2.5 Applications 2.5.1 Sets of distinct representatives 2.5.2 PERT 2.5.3 Optimum communication spanning treeChapter 3. Dynamic programming 3.1 Introduction 3.2 Knapsack problem 3.3 Two-dimensional knapsack problem 3.4 Minimum-cost alphabetic tree 3.5 SummaryChapter 4. Backtracking 4.1 Introduction 4.2 Estimating the efficiency of backtracking 4.3 Branch and bound 4.4 Game-treeChapter 5. Binary tree 5.1 Introduction 5.2 Huffman's tree 5.3 Alphabetic tree 5.4 Hu-Tucker algorithm 5.5 Feasibility and optimality 5.6 Garsia and Wachs' algorithm 5.7 Regular cost function 5.8 T-ary tree and other resultsChapter 6. Heuristic and near optimum 6.1 Greedy algorithm 6.2 Bin-packing 6.3 Job-scheduling 6.4 Job-scheduling (tree-constraints)Chapter 7. Matrix multiplication 7.1 Strassen's matrix multiplication 7.2 Optimum order of multiplying matrices 7.3 Partitioning a convex polygon 7.4 The heuristic algorithmChapter 8. NP-complete 8.1 Introduction 8.2 Polynomial algorithms 8.3 Nondeterministic algorithms 8.4 NP-complete problems 8.5 Facing a new problemChapter 9. Local indexing algorithms 9.1 Mergers of algorithms 9.2 Maximum flows and minimum cuts 9.3 Maximum adjacency and minimum separationChapter 10. Gomory-Hu tree 10.1 Tree edges and tree links 10.2 Contraction 10.3 Domination 10.4 Equivalent formulations 10.4.1 Optimum mergers of companies 10.4.2 Optimum circle partition 10.5 Extreme stars and host-feasible circles 10.6 The high-level approach 10.7 Chop-stick method 10.8 Relationship between phases 10.9 The staircase diagram 10.10 Complexity issuesAppendix A. Comments on Chapters 2, 5 & 6 A.1 Ancestor trees A.2 Minimum surface or plateau problem A.3 Comments on binary trees in chapter 5 A.3.1 A simple proof of the Hu-Tucker algorithm A.3.2 Binary search trees A.3.3 Binary search on a tape A.4 Comments on §6.2, bin-packingAppendix B. Network algebra

Produkt-Details

• Erscheint lt. Verlag: 26.4.2012
• Reihe/Serie: Dover Books on Computer Science
• Sprache: englisch
• Maße: 170 x 170 mm
• Themenwelt: Mathematik / Informatik ► Mathematik
• ISBN-13: 9780486152943 / 9780486152943