A Near-Tight Bound for the Online Steiner Tree Problem in Graphs of Bounded Asymmetry

The edge asymmetry of a directed, edge-weighted graph is defined as the maximum ratio of the weight of antiparallel edges in the graph, and can be used as a measure of the heterogeneity of links in a data communication network. In this paper we provide a near-tight upper bound on the competitive ratio of the Online Steiner Tree problem in graphs of bounded edge asymmetry . This problem has applications in efficient multicasting over networks with non-symmetric links. We show an improved upper bound of O min max log k log , log k log log k , k on the competitive ratio of a simple greedy algorithm, for any request sequence of k terminals. The result almost matches the lower bound of min max log k log , log k log log k , k1(where is an arbitrarily small constant) due to Faloutsos et al. [8] and Angelopoulos [3].

• Type: Conference
• Year: 2008
• Where: ESA
• Authors: Spyros Angelopoulos
• Keywords: Algorithms, Edge Asymmetry, ESA 2008, Min Max Log, Upper Bound