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

https://doi.org/10.1016/S0022-0000(76)80045-1Get rights and content
Under an Elsevier user license
open archive

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.

Cited by (0)

*

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Energy Research and Development Administration, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately-owned rights.

†

Work performed under the auspices of the U.S. Energy Research and Development Administration under Contract No. W-7405-Eng-48.

‡

Research supported by a National Science Foundation Graduate Fellowship and NSF Grant GJ-1052 while in the Program in Applied Mathematics and the Department of Electrical Engineering at Princeton University.

Copyright © 1976 Academic Press, Inc. Published by Elsevier Inc. All rights reserved.