Combinatorial Algorithms / Edition 2

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Overview


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 "Chop-Sticks" 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.
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Product Details

  • ISBN-13: 9780486419626
  • Publisher: Dover Publications
  • Publication date: 4/15/2002
  • Series: Dover Books on Computer Science Series
  • Edition description: Enlarged Edition
  • Edition number: 2
  • Pages: 368
  • Product dimensions: 6.64 (w) x 9.32 (h) x 0.80 (d)

Table of Contents

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-search
Chapter 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 tree
Chapter 3. Dynamic programming
  3.1 Introduction
  3.2 Knapsack problem
  3.3 Two-dimensional knapsack problem
  3.4 Minimum-cost alphabetic tree
  3.5 Summary
Chapter 4. Backtracking
  4.1 Introduction
  4.2 Estimating the efficiency of backtracking
  4.3 Branch and bound
  4.4 Game-tree
Chapter 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 results
Chapter 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 algorithm
Chapter 8. NP-complete
  8.1 Introduction
  8.2 Polynomial algorithms
  8.3 Nondeterministic algorithms
  8.4 NP-complete problems
  8.5 Facing a new problem
Chapter 9. Local indexing algorithms
  9.1 Mergers of algorithms
  9.2 Maximum flows and minimum cuts
  9.3 Maximum adjacency and minimum separation
Chapter 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 issues
Appendix 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 ยง6.2, bin-packing
Appendix B. Network algebra
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