Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs

Abstract

Chordal graphs arise naturally in the study of Gaussian elimination on sparse symmetric matrices; acyclic hypergraphs arise in the study of relational data bases. Rose, Tarjan and Lueker [SIAM J. Comput., 5 (1976), pp. 266–283] have given a linear-time algorithm to test whether a graph is chordal, which Yannakakis has modified to test whether a hypergraph is acyclic. Here we develop a simplified linear-time test for graph chordality and hypergraph acyclicity. The test uses a new kind of graph (and hypergraph) search, which we call maximum cardinality search A variant of the method gives a way to selectively reduce acyclic hypergraphs, which is needed for evaluating queries in acyclic relational data bases.

Keywords

  1. graph algorithm
  2. acyclic data base scheme
  3. sparse Gaussian elimination
  4. graph search
  5. hypergraph

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cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 566 - 579
ISSN (online): 1095-7111

History

Submitted: 7 October 1982
Published online: 13 July 2006

Keywords

  1. graph algorithm
  2. acyclic data base scheme
  3. sparse Gaussian elimination
  4. graph search
  5. hypergraph

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