Document Type

Article

Publication Date

1998

DOI

10.1016/s0166-218x(97)00085-1

Publication Title

Discrete Applied Mathematics

Volume

81

Issue

1-3

Pages

191-215

Abstract

A number of problems in mobile computing, group-based collaboration, automated theorem proving, networking, scheduling, and cluster analysis suggested the study of graphs featuring certain “local density” characteristics. Typically, the notion of local density is equated with the absence of chordless paths of length three or more. Recently, a new metric for local density has been proposed, allowing a number of such induced paths to occur. More precisely, a graphG is called P4-sparse if no set of five vertices inG induces more than one chordless path of length three. P4-sparse graphs generalize the well-known class of cographs corresponding to a more stringent local density metric. One remarkable feature of P4-sparse graphs is that they admit a tree representation unique up to isomorphism. In this work we present a parallel algorithm to recognize P4-sparse graphs and show how the data structures returned by the recognition algorithm can be used to construct the corresponding tree representation. With a graphG= (V, E) with¦V¦=n and¦E¦= m as input, our algorithms run inO(log n) time usingO((n2 + mn)/ log n) processors in the EREW-PRAM model.

Comments

Elsevier open archive. Copyright © 1998 Published by Elsevier B.V. All rights reserved.

Original Publication Citation

Lin, R., & Olariu, S. (1998). A fast parallel algorithm to recognize P4-sparse graphs. Discrete Applied Mathematics, 81(1-3), 191-215. doi:10.1016/s0166-218x(97)00085-1

ORCID

0000-0002-3776-216X (Olariu)

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