New encodings achieve 2n + 2√(2n) + O(n^{1/3}) clauses for AtMostOne, refuting prior optimality conjectures, with a matching lower bound and grid compression yielding 2n + o(n) clauses for AtMost_k when k = o(n^{1/3}).
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Near-Optimal Encodings of Cardinality Constraints
New encodings achieve 2n + 2√(2n) + O(n^{1/3}) clauses for AtMostOne, refuting prior optimality conjectures, with a matching lower bound and grid compression yielding 2n + o(n) clauses for AtMost_k when k = o(n^{1/3}).