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Incrementing Bipartite Digraph Edge-Connectivity

Author

Listed:
  • Harold N. Gabow

    (University of Colorado at Boulder)

  • Tibor Jordán

    (Eötvös University)

Abstract

This paper solves the problem of increasing the edge-connectivity of a bipartite digraph by adding the smallest number of new edges that preserve bipartiteness. A natural application arises when we wish to reinforce a 2-dimensional square grid framework with cables. We actually solve the more general problem of covering a crossing family of sets with the smallest number of directed edges, where each new edge must join the blocks of a given bipartition of the elements. The smallest number of new edges is given by a min-max formula that has six infinite families of exceptional cases. We discuss a problem on network flows whose solution has a similar formula with three infinite families of exceptional cases. We also discuss a problem on arborescences whose solution has five infinite families of exceptions. We give an algorithm that increases the edge-connectivity of a bipartite digraph in the same time as the best-known algorithm for the problem without the bipartite constraint: O(km log n) for unweighted digraphs and O(nm log (n 2/m)) for weighted digraphs, where n, m and k are the number of vertices and edges of the given graph and the target connectivity, respectively.

Suggested Citation

  • Harold N. Gabow & Tibor Jordán, 2000. "Incrementing Bipartite Digraph Edge-Connectivity," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 449-486, December.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:4:d:10.1023_a:1009885511650
    DOI: 10.1023/A:1009885511650
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    Cited by:

    1. Mehdy Roayaei & Mohammadreza Razzazi, 2017. "Augmenting weighted graphs to establish directed point-to-point connectivity," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 1030-1056, April.

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