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A network isolation algorithm

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  • M. Bellmore
  • G. Bennington
  • S. Luhore

Abstract

A set of edges D called an isolation set, is said to isolate a set of nodes R from an undirected network if every chain between the nodes in R contains at least one edge from the set D. Associated with each edge of the network is a positive cost. The isolation problem is concerned with finding an isolation set such that the sum of its edge costs is a minimum. This paper formulates the problem of determining the minimal cost isolation as a 0–1 integer linear programming problem. An algorithm is presented which applies a branch and bound enumerative scheme to a decomposed linear program whose dual subproblems are minimal cost network flow problems. Computational results are given. The problem is also formulated as a special quadratic assignment problem and an algorithm is presented that finds a local optimal solution. This local solution is used for an initial bound.

Suggested Citation

  • M. Bellmore & G. Bennington & S. Luhore, 1970. "A network isolation algorithm," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 17(4), pages 461-469, December.
    • Handle: RePEc:wly:navlog:v:17:y:1970:i:4:p:461-469
    DOI: 10.1002/nav.3800170405
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