An approximation algorithm for the balanced capacitated minimum spanning tree problem

Document Type : Article

Authors

Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, P.O. Box 15875-4413, Iran

10.24200/sci.2020.54242.3663

Abstract

The capacitated minimum spanning tree problem (CMSTP), a well-known combinatorial optimiza-
tion problem, holds a central place in telecommunication network design. This problem is to fi nd 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. We show this problem is NP-hard and present two approximation algorithms,
in this paper.
Considering the maximum order of the subtrees Q, we provide a (3 - 1
/Q)-approximation algorithm to find a
balanced solution. We improve this result to a (2:5 + \epsilon)-approximation algorithm (for every given \epsilon > 0), in
the 2d-Euclidean spaces. Also, we present a polynomial time approximation scheme (PTAS) for CMSTP.

Keywords


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