An Efficient Polynomial Time Approximation Scheme for the Constrained Minimum Spanning Tree Problem Using Matroid Intersection

Abstract

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.