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

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.