# Network Models

**By**

- Gerard Meurant

The set of papers in this Handbook reflect the rich 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.

### Book information

- Published: May 1995
- Imprint: ELSEVIER
- ISBN: 978-0-444-89292-8

### Table of Contents

**Applications of Network Optimization**(R.K. Ahuja

*et al.*). Preliminaries. Shortest paths. Maximum flows. Minimum cost flows. The assignment problem. Matchings. Minimum spanning trees. Convex cost flows. Generalized flows. Multicommodity flows. The travelling salesman problem. Network design.

**Primal Simplex Algorithms for Minimum Cost Network Flows**(R.V. Helgason, J.L. Kennington). Primal simplex algorithm. Linear network models. Generalized networks. Multicommodity networks. Networks with side constraints.

**Matching**(A.M.H. Gerards). Finding a matching of maximum cardinality. Bipartite matching duality. Non-bipartite matching duality. Matching and integer and linear programming. Finding maximum and minimum weight matchings. General degree constraints. Other matching algorithms. Applications of matchings. Computer implementations and heuristics.

**The Travelling Salesman Problem**(M. Jünger, G. Reinelt, G. Rinaldi). Related problems. Practical applications. Approximation algorithms for the TSP. Relaxations. Finding optimal and provably good solutions. Computation.

**Parallel Computing in Network Optimization**(D. Bertsekas

*et al.*). Linear network optimization. Nonlinear network optimization.

**Probabilistic Networks and Network Algorithms**(T.L. Snyder, J.M. Steele). Probability theory of network characteristics. Probabilistic network algorithms. Geometric networks.

**A Survey of Computational Geometry**(J.S.B. Mitchell, S. Suri). Fundamental structures. Geometric graphs. Path planning. Matching, travelling salesman, and watchman routes. Shape analysis, computer vision, and pattern matching.

**Algorithmic Implications of the Graph Minor Theorem**(D. Bienstock, M.A. Langston). A brief outline of the graph minors project. Treewidth. Pathwidth and cutwidth. Disjoint paths. Challenges to practicality.

**Optimal Trees**(T.L. Magnanti, L.A. Wolsey). Tree optimization problems. Minimum spanning trees. Rooted subtrees of a tree. Polynomially solvable extensions/variations. The Steiner tree problem. Packing subtrees of a tree. Packing subtrees of a general graph. Trees-on-trees.

**Design of Survivable Networks**(M. Grötschel, C.L. Monma, M. Stoer). Overview. Motivation. Integer programming models of survivability. Structural properties and heuristics. Polynomially solvable special cases. Polyhedral results. Computational results. Directed variants of the general model.

**Network Reliability**(M.O. Ball, C.J. Colbourn, J.S. Provan). Motivation. Computational complexity and relationships among problems. Exact computation of reliability. Bounds on network reliability. Monte Carlo methods. Performability analysis and multistate network systems. Using computational techniques in practice.

**Biographical Information. Subject Index. Contents of Previous Volumes.**