Algorithms for generating convex sets in acyclic digraphs

Authors:
P. Balister;S. Gerke;G. Gutin;A. Johnstone;J. Reddington;E. Scott;A. Soleimanfallah;A. Yeo
Affiliations:
Department of Mathematical Sciences, University of Memphis, TN 38152-3240, USA;Department of Mathematics, Royal Holloway, University of London, Egham, TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, UK;Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, UK
Venue:
Journal of Discrete Algorithms
Year:
2009

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Abstract

A set X of vertices of an acyclic digraph D is convex if X@A and there is no directed path between vertices of X which contains a vertex not in X. A set X is connected if X@A and the underlying undirected graph of the subgraph of D induced by X is connected. Connected convex sets and convex sets of acyclic digraphs are of interest in the area of modern embedded processor technology. We construct an algorithm A for enumeration of all connected convex sets of an acyclic digraph D of order n. The time complexity of A is O(n@?cc(D)), where cc(D) is the number of connected convex sets in D. We also give an optimal algorithm for enumeration of all (not just connected) convex sets of an acyclic digraph D of order n. In computational experiments we demonstrate that our algorithms outperform the best algorithms in the literature.