PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Algorithms for generating convex sets in acyclic digraphs
P. Balister, S. Gerke, Gregory Gutin, A. Johnstone, J. Reddington, E. Scott, A. Soleimanfallah and A. Yeo
Discrete Algorithms 2008.

Abstract

A set $X$ of vertices of an acyclic digraph $D$ is convex if $X\neq \emptyset$ and there is no directed path between vertices of $X$ which contains a vertex not in $X$. A set $X$ is connected if $X\neq \emptyset$ 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 $\cal A$ for enumeration of all connected convex sets of an acyclic digraph $D$ of order $n$. The time complexity of $\cal A$ is $O(n\cdot cc(D))$, 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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:5208
Deposited By:Gregory Gutin
Deposited On:24 March 2009