An Efficient Encoding of the at-most-one Constraint

One of the most widely used constraint during the process of translating a practical problem into an equivalent SAT instance is the at-most-one (AMO) constraint. Besides a brief survey of well-known AMO encodings, we will point out the relationship among several AMO encodings the relaxed ladder, sequential, regular and ladder encodings. Therefore, it could help SAT community, especially researchers working in SAT encoding to avoid confusing among these encodings. The major goal of this paper is to propose a new encoding for the AMO constraint, named the bimander encoding which can be easily extended to cardinality constraints. Experimental results reveal that the proposed method is a significantly competitive one among other recently efficient methods. We will prove that the bimander encoding allows the unit propagation to achieve arc consistency. Furthermore, we will show that one of special case of bimander encoding outperforms the binary encoding, a well-known AMO encoding, in all experiments.