The HyperTrac Project: Recent Progress and Future Research Directions on Hypergraph Decompositions

TL;DR

This paper reviews recent advances in hypergraph decompositions for CSPs, highlighting progress and future research directions to improve tractability and computation of these decompositions.

Contribution

It summarizes recent progress in hypergraph decomposition techniques and outlines promising future research directions in the field.

Findings

Progress in hypergraph decomposition methods for CSPs

Identification of tractable CSP fragments

Future research avenues outlined

Abstract

Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore, various forms of hypergraph decompositions have been proposed in the literature to identify tractable fragments of CSPs. However, also the computation of a concrete hypergraph decomposition is a challenging task in itself. In this paper, we report on recent progress in the study of hypergraph decompositions and we outline several directions for future research.