Computing hypergraph width measures exactly

TL;DR

This paper introduces a general exact exponential algorithm for computing hypergraph width measures, establishing a connection with tree decompositions to adapt known graph algorithms to hypergraphs, enabling efficient exact computations.

Contribution

It presents a unified approach for exact exponential algorithms for hypergraph width measures, leveraging tree decomposition techniques.

Findings

Algorithms for generalized hypertree-width in O*(2^n) time

Algorithms for fractional hypertree-width in O(m*1.734601^n) time

Connection established between hypergraph width measures and tree decompositions

Abstract

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2^n) and compute the fractional hypertree-width of H in time O(m*1.734601^n).