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

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 ` 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( √ log n)-approximation algorithm for this problem with uniform degree bounds of Könemann, Levin, and Sinha (Könemann et al., 2003) 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 (Ren et al., 2008) under a natural assumption can be reduced to this non-uniform case of the BDST problem.