Decomposition Techniques for Subgraph Matching

TL;DR

This paper introduces a hybrid decomposition approach with heuristics for solving the subgraph isomorphism problem within constraint programming, outperforming existing methods on sparse graphs.

Contribution

It proposes a novel hybrid decomposition technique with heuristics tailored for the subgraph isomorphism problem, improving solution efficiency for sparse graphs.

Findings

Outperforms state-of-the-art matching algorithms on sparse graphs

Effective decomposition reduces search space and improves solution times

Hybrid approach combines static heuristics with dynamic decomposition

Abstract

In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques in the presence of global constraints. In particular, we solve the subgraph isomorphism problem. Further we design specific heuristics for this hard problem, exploiting its special structure to achieve decomposition. The underlying idea is to precompute a static heuristic on a subset of its constraint network, to follow this static ordering until a first problem decomposition is available, and to switch afterwards to a fully propagated, dynamically decomposing search. Experimental results show that, for sparse graphs, our decomposition method solves more instances than dedicated, state-of-the-art matching algorithms or standard constraint programming approaches.