An algorithm for finding input-output constrained convex sets in an acyclic digraph

Authors:
G. Gutin;A. Johnstone;J. Reddington;E. Scott;A. Yeo
Affiliations:
Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom;Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom
Venue:
Journal of Discrete Algorithms
Year:
2012

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Abstract

A set X of vertices of an acyclic graph is convex if any vertex on a directed walk between elements of X is itself in X. We construct an algorithm for generating all input-output constrained convex (IOCC) sets in an acyclic digraph, which uses several novel ideas. We show that the time complexity of our algorithm significantly improves the best one known from the literature. IOCC sets of acyclic digraphs are of interest in the area of modern embedded processor technology.