Improved Approximation Algorithms for the Single-Sink Buy-at-Bulk Network Design Problems
Consider a given undirected graph G=(V, E) with non-negative edge costs, a root node r ∈ V, and a set D ⊆ V of demands with d v representing the units of flow that demand v ∈ 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 α K , where α K is less than 65.49 for all K. In particular, α 2 < 12.7, α 3 < 18.2, α 4 < 23.8, α 5 < 29.3, α 6 < 33.9.
KeywordsApproximation Ratio Steiner Tree Network Design Problem Single Path Euler Tour
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