On testing consecutive-ones property in parallel

Abstract

The consecutive-ones property problem has many important applications in the field of discrete algorithms, including the physical mapping problem in computational molecular biology. A (0, 1)-matrix is said to satisfy the consecutive-ones property if there is a permutation of the rows of the matrix such that in each column all non-zero entries are adjacent. The problem of determining such a permutation, if one exists, is the consecutive-ones property problem. The classic algorithm for solving this problem is a linear time sequential algorithm of Booth and Lueker (1976) which is known to be based on the PQ-tree data structure. In this paper we present a new algorithm for this problem using a divide-and-conquer method that employs a graph-theoretic data structure known as Tutte decomposition, i.e., decomposition of graphs into 3-connected components. Our algorithm enjoys the property that it efficiently parallelizes using the standard PRAM parallel computational model, while avoiding the complex implementations associated with PQ-trees. Our algorithm is more work efficient than previous parallel solutions, improving on the known processor bounds.