Papers › A Heuristic for Direct Product Graph Decomposition
A Heuristic for Direct Product Graph Decomposition
Luca Calderoni, Luciano Margara, Moreno Marzolla
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In this paper we describe a heuristic for decomposing a directed graph into factors according to the direct product (also known as Kronecker, cardinal or tensor product). Given a directed, unweighted graph~G with adjacency matrix Adj(G), our heuristic searches for a pair of graphs~G₁ and~G₂ such that G = G₁ ⊗G₂, where G₁ ⊗G₂ is the direct product of~G₁ and~G₂. For undirected, connected graphs it has been shown that graph decomposition is "at least as difficult" as graph isomorphism; therefore, polynomial-time algorithms for decomposing a general directed graph into factors are unlikely to exist. Although graph factorization is a problem that has been extensively investigated, the heuristic proposed in this paper represents -- to the best of our knowledge -- the first computational approach for general directed, unweighted graphs. We have implemented our algorithm using the MATLAB environment; we report on a set of experiments that show that the proposed heuristic solves reasonably-sized instances in a few seconds on general-purpose hardware.
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