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The set of papers in this handbook reflect the varied theory and wide range of applications of network models. Two of the most vibrant applications areas of network models are telecommunications and transportation. Several chapters explicitly model issues arising in these problem domains. Research on network models has been closely aligned with the field of computer science both in developing data structures for efficiently implementing network algorithms and in analyzing the complexity of network problems and algorithms. The basic structure underlying all network problems is a graph. Thus, historically, there have been strong ties between network models and graph theory. A companion volume in the "Handbook" series, entitled "Network Routing", examines problems related to the movement of commodities over a network. The problems treated arise in several application areas including logistics, telecommunications, facility location, VLSI design, and economics.

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Contents
Preface = ⅴ
CHAPTER 1 Applications of Network Optimization / R. K. Ahuja ; T. L. Magnanti ; J. B. Orlin ; M. R. Reddy = 1
  1. Introduction = 1
  2. Preliminaries = 3
  3. Shortest paths = 5
  4. Maximum flows = 17
  5. Minimum cost flows = 27
  6. The assignment problem = 35
  7. Matchings = 38
  8. Minimum spanning trees = 43
  9. Convex cost flows = 49
  10. Generalized flows = 54
  11. Multicommodity flows = 58
  12. The traveling salesman problem = 62
  13. Network design = 69
  14. Summary = 74
  References = 75
CHAPTER 2 Primal Simplex Algorithms for Minimum Cost Network Flows / R. V. Helgason ; J. L. Kennington = 85
  1. Introduction = 85
  2. Primal simplex algorithm = 93
  3. Linear network models = 95
  4. Generalized networks = 108
  5. Multicommodity networks = 116
  6. Networks with side constraints = 125
  7. Reference notes = 130
  Reference = 132
CHAPTER 3 Matching / A. M. H. Gerards = 135
  1. Introduction = 135
  2. Finding a matching of maximum cardinality = 142
  3. Bipartite matching duality = 152
  4. Non-bipartite matching duality = 159
  5. Matching and integer and linear programming = 164
  6. Finding maximum and minimum weight matchings = 172
  7. General degree constraints = 179
  8. Other matching algorithms = 191
  9. Applications of matchings = 202
  10. Computer implementations and heuristics = 207
  References = 212
CHAPTER 4 The Traveling Salesman Problem / M. J u ·· nger ; G. Reinelt ; G. Rinaldi = 225
  1. Introduction = 225
  2. Related problems = 227
  3. Practical applications = 231
  4. Approximation algorithms = 234
  5. Relaxations = 268
  6. Finding optimal and provably good solutions = 294
  7. Computation = 314
  References = 323
CHAPTER 5 Parallel Computing in Network Optimization / D. Bertsekas ; D. Casta n ~ on ; J. Eckstein ; S. Zenios = 331
  1. Introduction = 331
  2. Linear network optimization = 339
  3. Nonlinear network optimization = 370
  4. Conclusions = 393
  References = 394
CHAPTER 6 Probabilistic Networks and Network Algorithms / T. L. Snyder ; J. M. Steele = 401
  1. Introduction = 401
  2. Probability theory of network characteristics = 403
  3. Probabilistic network algorithms = 410
  4. Geometric networks = 415
  5. Concluding remarks = 421
  References = 421
CHAPTER 7 A Survey of Computational Geometry / J. S. B. Mitchell ; S. Suri = 425
  1. Introduction = 425
  2. Fundamental structures = 426
  3. Geometric graphs = 432
  4. Path planning = 439
  5. Matching, traveling salesman, and watchman routes = 459
  6. Shape analysis, computer vision, and pattern matching = 462
  7. Conclusion = 468
  References = 469
CHAPTER 8 Algorithmic Implications of the Graph Minor Theorem / D. Bienstock ; M. A. Langston = 481
  1. Introduction = 481
  2. A brief outline of the graph minors project = 481
  3. Treewidth = 486
  4. Pathwidth and cutwidth = 493
  5. Disjoint paths = 459
  6. Challenges to practicality = 498
  References = 501
CHAPTER 9 Optimal Trees / T. L. Magnanti ; L. A. Wolsey = 503
  1. Introduction = 503
  2. Tree optimization problems = 507
  3. Minimum spanning trees = 518
  4. Rooted subtrees of a tree = 540
  5. Polynomially solvable extensions / variations = 548
  6. The Steiner tree problem = 557
  7. Packing subtrees of a tree = 572
  8. Packing subtrees of a general graph = 585
  9. Trees-on-trees = 598
  10. Summary = 604
  11. Notes and references = 607
  References = 611
CHAPTER 10 Design of Survivable Networks / M. Gr o ·· tschel ; C. L. Monma ; M. Stoer = 617
  1. Overview = 617
  2. Motivation = 618
  3. Integer programming models of survivability = 620
  4. Structural properties and heuristics = 627
  5. Polynomially solvable special cases = 634
  6. Polyhedral results = 638
  7. Computational results = 648
  8. Directed variants of the general model = 663
  References = 669
CHAPTER 11 Network Reliability / M. O. Ball ; C. J. Colbourn ; J. S. Provan = 673
  1. Motivation = 673
  2. Computatinal complexity and relationships among problems = 680
  3. Exact computation of reliability = 687
  4. Bounds on network reliability = 696
  5. Monte Carlo methods = 714
  6. Performability analysis and multistate network systems = 722
  7. Using computational techniques in practice = 740
  References = 745
Biographical Information = 763
Subject Index = 769
Contents of Previous Volumes = 783