Primal-target neural net heuristics for the hypergraph k-coloring problem

The hypergraph strong coloring problem (HC) is an NP-hard problem on hypergraphs arising naturally in applications involving conflict-free access of data in parallel memory systems. There has been much work on solving graph optimization problems using neural networks; however, almost none on solving hypergraph problems. Hypergraph problems present interesting challenges to neural networks because they involve higher-order structures than those in graphs In this paper we introduce a primal-target approach to solve hard combinatorial problems having inequality constraints. We consider the variant of HC,-the maximum induced subhypergraph strong k-coloring problem (HkC). We present two primal-target algorithms that map HkC onto a Hopfield network. The first algorithm uses a larger set of target variables which leads to a more elaborate search mechanism. Experiments showed that both algorithms, PT1 and PT2, were competitive, with a naive optimal algorithm on small instances of random hypergraphs, while being significantly faster. Algorithm PT1 scaled significantly better to larger hypergraphs than PT2, while PT2 ran faster than PT1