Algorithms for P4-Comparability Graph Recognition and Acyclic P4-Transitive Orientation

  • Authors:

  • Stavros D. Nikolopoulos;Leonidas Palios

  • Affiliations:

  • Department of Computer Science, University of Ioannina, 45110 Ioannina, Greece;Department of Computer Science, University of Ioannina, 45110 Ioannina, Greece

  • Venue:
  • Algorithmica
  • Year:
  • 2004

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Abstract

We consider two problems pertaining to P4-comparabilitygraphs, namely, the problem of recognizing whether a simpleundirected graph is a P4-comparability graph and theproblem of producing an acyclic P4-transitiveorientation of a P4-comparability graph. These problemshave been considered by Hoàng and Reed who describedO(n4)- and O(n5)-time algorithms for theirsolution, respectively, where n is the number of vertices of theinput graph. Faster algorithms have recently been presented byRaschle and Simon, and by Nikolopoulos and Palios; the timecomplexity of these algorithms for either problem is O(n +m2), where m is the number of edges of the graph. Inthis paper we describe O(n m)-time and O(n + m)-space algorithmsfor the recognition and the acyclic P4-transitiveorientation problems on P4-comparability graphs. Thealgorithms rely on properties of the P4-components of agraph, which we establish, and on the efficient construction of theP4-components by means of the BFS-trees of thecomplement of the graph rooted at each of its vertices, withouthowever explicitly computing the complement. Both algorithms aresimple and use simple data structures.