Incrementing Bipartite Digraph Edge-Connectivity

Harold N. Gabow, T. Jordán

Research output: Contribution to journalArticle

6 Citations (Scopus)

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(n2/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.

Original languageEnglish
Pages (from-to)449-486
Number of pages38
JournalJournal of Combinatorial Optimization
Volume4
Issue number4
Publication statusPublished - 2000

Fingerprint

Edge-connectivity
Digraph
Cables
Network Flow
Min-max
Cable
Exception
Join
Connectivity
Covering
Grid
Target
Family
Graph in graph theory

Keywords

  • Connectivity augmentation
  • Crossing family
  • Graph algorithms
  • Min-max theorems
  • Rigidity
  • Square grid frame-work

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

Cite this

Incrementing Bipartite Digraph Edge-Connectivity. / Gabow, Harold N.; Jordán, T.

In: Journal of Combinatorial Optimization, Vol. 4, No. 4, 2000, p. 449-486.

Research output: Contribution to journalArticle

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