The non-uniform Bounded Degree Minimum Diameter Spanning Tree problem with an application in P2P networking

Abstract

This paper considers the Bounded Degree Minimum Diameter Spanning Tree problem (BDST problem) with non-uniform degree bounds. In this problem, we are given a metric length function ℓ over a set V of n nodes and a degree bound Bv for each v∈V, and want to find a spanning tree with minimum diameter such that each node v has degree at most Bv. We present a simple extension of an O(logn)-approximation algorithm for this problem with uniform degree bounds of Könemann, Levin, and Sinha [J. Könemann, A. Levin, A. Sinha, Approximating the degree-bounded minimum diameter spanning tree problem, in: Algorithmica, Springer, 2003, pp. 109–121] to work with non-uniform degree bounds. We also show that this problem has an application in the peer-to-peer content distribution. More specifically, the Minimum Delay Mesh problem (MDM problem) introduced by Ren, Li and Chan [D. Ren, Y.-T. Li, S.-H. Chan, On reducing mesh delay for peer-to-peer live streaming, in: INFOCOM, 2008, pp. 1058–1066] under a natural assumption can be reduced to this non-uniform case of the BDST problem.