Polynomial Time Approximation Schemes for the Constrained Minimum Spanning Tree Problem

Yen Hung Chen

doi:10.1155/2012/394721

Abstract

LetG=(V,E)be an undirected graph with a weight function and a cost function on edges. The constrained minimum spanning tree problem is to find a minimum cost spanning treeTinGsuch that the total weight inTis at most a given boundB. In this paper, we present two polynomial time approximation schemes (PTASs) for the constrained minimum spanning tree problem.

Highlights

Motivated by the applications of quality of service QoS routing and multicasting, several multiple criteria problems have been studied see [1,2,3,4,5,6] and references therein
Given an undirected graph G V, E and two independent minimization criteria with a bound on the first criterion, a generic bicriteria network design problem involves the minimization of the second criterion but satisfies the bound on the first criterion among all possible subgraphs from G 5
The degree of a node is the number of nodes adjacent to this node, and the maximum degree of a graph is maximum over the degrees of all nodes in the subgraph

Summary

Introduction

Motivated by the applications of quality of service QoS routing and multicasting, several multiple criteria problems have been studied see [1,2,3,4,5,6] and references therein. Ravi and Goemans 10 presented a 2, 1 -approximation algorithm to solve the CMST problem in O |E|log2|V | |V |log3|V | time and improved the ratio to 1 ε, 1 , where the time complexity is O |V |O 1/ε |E|log2|V | |V |log3|V | for any constant ε > 0. Chen and Xue [18, 19] used a similar method to design PTASs for the k-pair delay constrained minimum cost routing problem and the weight constrained Steiner tree problem in series-parallel graphs These algorithms are based on the rounding and scaling strategy that is offered by Hassin 14.

PTASs for the Constrained Minimum Spanning Tree Problem

Conclusion