An approximation algorithm for the balanced capacitated minimum spanning tree problem

Capacitated Minimum Spanning Tree Problem (CMSTP), a well-known combinatorial optimization problem, holds the central place in telecommunication network design. This problem involves finding a minimum cost spanning tree with an extra cardinality limitation on the orders of the subtrees incident to a certain root node. The Balanced Capacitated Minimum Spanning Tree Problem (BCMSTP) is a special case that aims to balance the orders of the subtrees. This problem is an NP-hard one and presents two approximation algorithms in this paper. By considering the maximum order of the subtrees Q, a (3 - 1/Q)-approximation algorithm was provided to find a balanced solution. This result was improved to a (2.5 + epsilon) approximation algorithm (for every given epsilon > 0) in the 2d-Euclidean spaces. Also, a Polynomial Time Approximation Scheme (PTAS) was presented for CMSTP. (C) 2021 Sharif University of Technology. All rights reserved.