An efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection
An efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection
复制标题
DOI：
10.1137/s0097539703426775
复制
发表时间：
2004-02
期刊：
影响因子：
--
通讯作者：
Refael Hassin;Asaf Levin
中科院分区：
文献类型：
--
作者：
Refael Hassin;Asaf Levin
给定一个无方向的图G =（v，e），| v | = n和| e | = m，e $中的每个边缘$ e \的非负整数ce和de，以及一个约束的d，约束的最小跨越树问题（CST）是找到一个生成树t =（v，et），以使$ \ sum_ {e _t} in e_t} d_e \ leq d $和$ \ sum_ {e _t} c_e $最小化。我们为此问题提供了有效的多项式时间近似方案（EPTA）。具体来说，对于每$ \ epsilon> 0 $，我们会出现$（1+ \ epsilon）$ - 近似算法，带有时间复杂性$ o（（（\ frac {1}} {\ epsilon} {\ epsilon}）^{o（\ frac {1}） {\ epsilon}）} n^4）$。我们的方法基于拉格朗日放松和矩形交集。
Given an undirected graph G=(V,E) with |V|=n and |E|=m, nonnegative integers ce and de for each edge $e \in E$, and a bound D, the constrained minimum spanning tree problem (CST) is to find a spanning tree T=(V,ET) such that $\sum_{e \in E_T} d_e \leq D$ and $\sum_{e \in E_T} c_e$ is minimized. We present an efficient polynomial time approximation scheme (EPTAS) for this problem. Specifically, for every $\epsilon>0$ we present a $(1+\epsilon)$-approximation algorithm with time complexity $O((\frac{1}{\epsilon})^{O(\frac{1}{\epsilon})}n^4)$. Our method is based on Lagrangian relaxation and matroid intersection.