Improved approximation algorithms for the single-sink buy-at-bulk network design problems

Abstract

Consider a given undirected graph G = (V, E) with nonnegative edge costs, a root node r ε V, and a set D C V of demands with dυ representing the units of flow that demand υ ∈ D wishes to send to the root. We are also given K types of cables, each with a specified capacity and cost per unit length. The single-sink buy-at-bulk (SSBB) problem asks for a low-cost installation of cables along the edges of G, such that the demands can simultaneously send their flows to sink/root r. The problem is studied with and without the restriction that the flow from a node must follow a single path to the sink (indivisibility constraint). We are allowed to install zero or more copies of a cable type on each edge. The SSBB problem is NP-hard. In this paper, we present a 145.6-approximation for the SSBB problem improving the previous best ratio of 216. For the divisible SSBB (DSSBB) problem, we improve the previous best ratio of 72.8 to αK, where αK is less than 65.49 for all K. In particular, α2 < 12.7, α3 < 18.2, α4 < 23.8, α5 < 29.3, α6 < 33.9. © Springer-Verlag Berlin Heidelberg 2004.