布尔 CSP 局部极大满足赋值计数问题的复杂性
计算复杂性
2016-05-17 v3
摘要
我们研究了在布尔域 {0,1} 上计数约束满足问题(CSP)的极大满足赋值问题的计算复杂性。如果一个满足赋值通过将某个 0 改为 1 而得到的任何新赋值都不满足，则该赋值是极大的。对于每个约束语言 Gamma，#MaximalCSP(Gamma) 表示给定约束属于 Gamma 的输入 CSP 时计数极大满足赋值的问题。我们给出了精确计数极大满足赋值问题的复杂性二分法，以及近似计数它们的复杂性三分法。相对于 #CSP(Gamma)（即计数所有满足赋值的问题），极大版本有时更容易但绝不会更难。这一发现与近期关于在二分图中近似计数极大独立集比计数所有独立集更难（在通常复杂性理论假设下）的发现形成对比。
引用
@article{arxiv.1509.03543,
title = {The complexity of counting locally maximal satisfying assignments of Boolean CSPs},
author = {Leslie Ann Goldberg and Mark Jerrum},
journal= {arXiv preprint arXiv:1509.03543},
year = {2016}
}
备注
V2 adds contextual material relating the results obtained here to earlier work in a different but related setting. The technical content is unchanged. V3 (this version) incorporates minor revisions. The title has been changed to better reflect what is novel in this work. This version has been accepted for publication in Theoretical Computer Science. 19 pages