How to make a square grid framework with cables rigid

Harold N. Gabow, Tibor Jordán

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

This paper solves the problem of making a bipartite digraph strongly connected by adding the smallest number of new edges that preserve bipartiteness. A result of Baglivo and Graver shows that this corresponds to making a two-dimensional square grid framework with cables rigid by adding the smallest number of new cables. We prove a min-max formula for the smallest number of new edges in the digraph problem and give a corresponding linear-time algorithm. We generalize these results to the problem of making an arbitrary digraph strongly connected by adding the smallest number of new edges, each of which joins vertices in distinct blocks of a given partition of the vertex set.

Original languageEnglish
Pages (from-to)649-680
Number of pages32
JournalSIAM Journal on Computing
Volume30
Issue number2
DOIs
Publication statusPublished - Jan 1 2000

Keywords

  • Connectivity augmentation
  • Graph algorithms
  • Min-max theorems
  • Rigidity
  • Square grid framework
  • Strong connectivity

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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