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

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