具有保守多数多态性的最小成本约束满足问题的常数因子近似
Constant-factor approximation of MinCostCSP with a conservative majority polymorphism
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中文总结 AI 辅助
研究MinCostCSP(A)的常数因子近似，针对承认保守多数多态性结构A，通过证明二分法迈出分类第一步，其二分法标准非代数条件且不可避免，还论证不存在相关代数条件。
中文摘要 AI 辅助
对于关系结构A，最小成本约束满足问题（记为MinCostCSP(A)）是：给定CSP(A)的一个实例，其变量-值对具有合理成本，找到一个使所选成本总和最小的实例解。对于精确最小化，Takhanov [STACS'10] 根据A对MinCostCSP(A)进行了分类。我们关注MinCostCSP(A)的常数因子近似。DeHaan、Huang和Lee最近表明，如果A不承认保守近一致多态性，那么MinCostCSP(A)不可常数因子近似 [APPROX'25]。我们通过证明承认保守多数（也称为3-近一致）多态性的结构A的二分法，朝着分类迈出了第一步。我们的二分法标准不是基于A的代数条件，但我们表明这是不可避免的。我们给出一个简单论证，证明不存在这样的条件。
英文摘要
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 first step towards a 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.
