反构件与复杂度二分法
计算复杂性
2011-11-30 v2 数据结构与算法
摘要
我们在复杂度归约中引入一种称为反构件(anti-gadget)的思想。这些组合构件具有擦除其他图片段的效果,仿佛我们成功包含了图构件的负副本。利用这一思想,我们证明了3-正则有向图G上配分函数Z(G)的复杂度二分法定理,其中每条边赋予复值二元函数f: {0,1}^2 → C。我们证明Z(G) = ∑_{σ: V(G) → {0,1}} ∏_{(u,v) ∈ E(G)} f(σ(u), σ(v))要么在多项式时间内可计算,要么是#P-完全的,具体取决于f。
引用
@article{arxiv.1108.3383,
title = {Gadgets and Anti-Gadgets Leading to a Complexity Dichotomy},
author = {Jin-Yi Cai and Michael Kowalczyk and Tyson Williams},
journal= {arXiv preprint arXiv:1108.3383},
year = {2011}
}
备注
26 pages, 14 figures, To appear at ITCS 2012, New version changes: minor copy edits, workaround for arXiv bug that made subscript references too large