Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

  • Authors:
  • Kellogg S. Booth;George S. Lueker

  • Affiliations:
  • -;-

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1976

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Abstract

A data structure called a PQ-tree is introduced. PQ-trees can be used to represent the permutations of a set U in which various subsets of U occur consecutively. Efficient algorithms are presented for manipulating PQ-trees. Algorithms using PQ-trees are then given which test for the consecutive ones property in matrices and for graph planarity. The consecutive ones test is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs. All of these algorithms require a number of steps linear in the size of their input.