Queue Layouts and Staircase Covers of Matrices

Abrams, Marc and Batongbacal, Alan and Ribler, Randy and Vazirani, Devendra and Heath, Lenwood S. and Pemmaraju, Sriram V. (1994) Queue Layouts and Staircase Covers of Matrices. Technical Report ncstrl.vatech_cs//TR-94-22, Computer Science, Virginia Polytechnic Institute and State University.

Abstract

A connection between a queue layout of an undirected graph and a staircase cover of its adjacency matrix is established. The connection is exploited to establish a number of combinatorial results relating the number of vertices, the number of edges, and the queue number of a queue layout. The staircase notion is generalized to that of an (h,w)- staircase, and an efficient algorithm to optimally cover a matrix with (h,w)- staircases is presented. The algorithm is applied to problems of monotonic subsequences and to the maxdominance problem of Atallah and Kosaraju.