Tractable Optimization Problems through Hypergraph-Based Structural Restrictions

TL;DR

This paper explores how hypergraph-based structural restrictions can identify larger classes of tractable instances for NP-hard optimization problems like constraint satisfaction, using acyclicity and decomposition techniques.

Contribution

It introduces new tractable classes of constraint satisfaction problems by leveraging hypergraph acyclicity and structural decomposition methods.

Findings

Larger classes of tractable instances identified

Hypergraph acyclicity enhances solvability

Structural decompositions improve solution approaches

Abstract

Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal solution is an NP-hard problem in general; yet, when restricted over classes of instances whose constraint interactions can be modelled via (nearly-)acyclic graphs, this problem is known to be solvable in polynomial time. In this paper, larger classes of tractable instances are singled out, by discussing solution approaches based on exploiting hypergraph acyclicity and, more generally, structural decomposition methods, such as (hyper)tree decompositions.