At-Most-One Constraints in Efficient Representations of Mutex Networks

TL;DR

This paper explores efficient encoding of At-Most-One constraints in mutex networks, improving SAT-based problem solving by detecting cliques and comparing different encodings for better performance.

Contribution

It introduces an online method for detecting cliques in mutex networks and compares various AMO encodings for enhanced efficiency.

Findings

Clique detection improves encoding efficiency.

Different AMO encodings impact SAT solving performance.

Online detection adapts to incremental mutex network updates.

Abstract

The At-Most-One (AMO) constraint is a special case of cardinality constraint that requires at most one variable from a set of Boolean variables to be set to TRUE. AMO is important for modeling problems as Boolean satisfiability (SAT) from domains where decision variables represent spatial or temporal placements of some objects that cannot share the same spatial or temporal slot. The AMO constraint can be used for more efficient representation and problem solving in mutex networks consisting of pair-wise mutual exclusions forbidding pairs of Boolean variable to be simultaneously TRUE. An on-line method for automated detection of cliques for efficient representation of incremental mutex networks where new mutexes arrive using AMOs is presented. A comparison of SAT-based problem solving in mutex networks represented by AMO constraints using various encodings is shown.