A linear-time algorithm for finding an ambitus

Bhubaneswar Mishra, R. E. Tarjan

Research output: Contribution to journalArticle

Abstract

We devise a linear-time algorithm for finding an ambitus ín an undirected graph. An ambitus is a cycle in a graph containing two distinguished vertices such that certain different groups of bridges (called B itp-, B itQ-, and B itPQ-bridges) satisfy the property that a bridge in one group does not interlace with any bridge in the other groups. Thus, an ambitus allows the graph to be cut into pieces, where, in each piece, certain graph properties may be investigated independently and recursively, and then the pieces can be pasted together to yield information about these graph properties in the original graph. In order to achieve a good time-complexity for such an algorithm employing the divide-and-conquer paradigm, it is necessary to find an ambitus quickly. We also show that, using ambitus, linear-time algorithms can be devised for abiding-path-finding and nonseparating-induced-cycle-finding problems.

Original languageEnglish (US)
Pages (from-to)521-554
Number of pages34
JournalAlgorithmica (New York)
Volume7
Issue number1-6
DOIs
StatePublished - Jun 1992

Fingerprint

Linear-time Algorithm
Graph in graph theory
Cycle
Divide and conquer
Undirected Graph
Time Complexity
Paradigm
Path
Necessary

Keywords

  • Abiding-path
  • All-bidirectional-edges problem
  • Ambitus
  • Bridge
  • Nonseparating induced cycle

ASJC Scopus subject areas

  • Applied Mathematics
  • Safety, Risk, Reliability and Quality
  • Software
  • Computer Graphics and Computer-Aided Design

Cite this

A linear-time algorithm for finding an ambitus. / Mishra, Bhubaneswar; Tarjan, R. E.

In: Algorithmica (New York), Vol. 7, No. 1-6, 06.1992, p. 521-554.

Research output: Contribution to journalArticle

Mishra, Bhubaneswar ; Tarjan, R. E. / A linear-time algorithm for finding an ambitus. In: Algorithmica (New York). 1992 ; Vol. 7, No. 1-6. pp. 521-554.
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