arXiv:2607.10667 · v2

Constant-factor approximation of MinCostCSP with a conservative majority polymorphism

首次提交 2026-07-12 17:24

版本更新 2026-11-03 17:14

雷达观测 2026-11-04 23:39

摘要

For a relational structure A, the Minimum Cost Constraint Satisfaction Problem is the following problem denoted by MinCostCSP(A): Given an instance of CSP(A) with rational costs on variable-value pairs, find a solution to the instance minimizing the sum of the chosen costs. For the exact minimization, a classification of MinCostCSP(A) in terms of A was established by Takhanov [STACS'10]. We focus on constant-factor approximations of MinCostCSP(A). DeHaan, Huang, and Lee recently showed that if A fails to admit a conservative near-unanimity polymorphism then MinCostCSP(A) is not constant-factor approximable [APPROX'25]. We provide a significant step towards a full classification, by proving a dichotomy for structures A admitting a conservative majority (also known as 3-near-unanimity) polymorphism. Our dichotomy criterion is not in terms of an algebraic condition on A but we show that this is unavoidable. We include a simple argument proving that no such condition exists.

作者备注：v2: improved presentation