Steiner trees, partial 2–trees, and minimum IFI networks

Joseph A. Wald, Charles J. Colbourn

Research output: Contribution to journalArticle

138 Scopus citations

Abstract

Minimum isolated failure immune networks are shown to be 2–trees. Further, subgraphs of 2‐trees are shown to be exactly those graphs which contain no subgraph homeomorphic to the four‐vertex complete graph. Together, these two characterizations yield a linear time algorithm for adding lines to a network to produce a minimum isolated failure immune network, whenever this is possible. This same algorithm, in conjunction with a linear time Steiner tree algorithm for 2‐tress, yields a linear time Steiner tree algorithm for partial 2‐tress. This contrasts with the known NP‐completeness of the Steiner tree problem for planar graphs.

Original languageEnglish (US)
Pages (from-to)159-167
Number of pages9
JournalNetworks
Volume13
Issue number2
DOIs
StatePublished - Jan 1 1983
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Hardware and Architecture
  • Computer Networks and Communications

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