Mutex Graphs and Multicliques: Reducing Grounding Size for Planning

TL;DR

This paper introduces a graph-theoretic method using multicliques to compactly represent mutex constraints, significantly reducing grounding size in ASP planning and improving solver efficiency.

Contribution

It proposes a novel multiclique-based approach for representing mutex constraints and an efficient approximation algorithm for multiclique covering, enhancing planning performance.

Findings

Substantially smaller grounding sizes achieved in ASP

Approximation algorithm effectively covers mutex graphs

Improved efficiency over previous SAT-based methods

Abstract

We present an approach to representing large sets of mutual exclusions, also known as mutexes or mutex constraints. These are the types of constraints that specify the exclusion of some properties, events, processes, and so on. They are ubiquitous in many areas of applications. The size of these constraints for a given problem can be overwhelming enough to present a bottleneck for the solving efficiency of the underlying solver. In this paper, we propose a novel graph-theoretic technique based on multicliques for a compact representation of mutex constraints and apply it to domain-independent planning in ASP. As computing a minimum multiclique covering from a mutex graph is NP-hard, we propose an efficient approximation algorithm for multiclique covering and show experimentally that it generates substantially smaller grounding size for mutex constraints in ASP than the previously known work in SAT.