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The at-most-k constraint is ubiquitous in combinatorial problems, andnumerous SAT encodings are available for the constraint. Prior experiments haveshown the competitiveness of the sequential-counter encoding for k $>$ 1, andhave excluded the parallel-counter encoding, which is more compact that thebinary-adder encoding, from consideration due to its incapability of enforcingarc consistency through unit propagation. This paper presents an experimentthat shows astounding performance of the binary-adder encoding for theat-most-k constraint.

Yet Another Comparison of SAT Encodings for the At-Most-K Constraint