A Fast Parallel Algorithm for the Maximal Independent Set Problem

Richard M. Karp, Avi Wigderson

Research output: Contribution to journalArticlepeer-review

157 Scopus citations

Abstract

A parallel algorithm is presented that accepts as input a graph G and produces a maximal independent set of vertices in G. On a P-RAM without the concurrent write or concurrent read features, the algorithm executes in O((log n)4) time and uses O((n/(log n))3) processors, where n is the number of vertices in G. The algorithm has several novel features that may find other applications. These include the use of balanced incomplete block designs to replace random sampling by deterministic sampling, and the use of a “dynamic pigeonhole principle” that generalizes the conventional pigeonhole principle.

Original languageEnglish
Pages (from-to)762-773
Number of pages12
JournalJournal of the ACM
Volume32
Issue number4
DOIs
StatePublished - 1 Oct 1985
Externally publishedYes

Keywords

  • Block designs
  • graph theory
  • independent sets
  • parallel computation

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