2015/04/30 by Erez Kantor, Kantor, Erez, Shay Kutten +1
Computer Science · Mathematics · #Algorithms and Data Compression #Binary logarithm #Combinatorics #Competitive analysis #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #Discrete mathematics #Distribution (mathematics) #FOS: Computer and information sciences #Mathematics #Omega #Optimization and Search Problems #Physics #Steiner tree problem #Upper and lower bounds #cs.DS
paper · pdf · doi:10.48550/arxiv.1504.08265
arxiv created 2015/04/30 · openalex publication_date 2015/04/30 · arxiv updated 2015/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lower and the upper bounds. One of them is the well studied continuous problem of the \em Rectilinear Steiner Arborescence (RSA). We improve the lower bound and the upper bound on the competitive ratio for RSA from O(log N) and Ω(√(log N)) to Θ((log N)/(log log N)), where N is the number of Steiner points. This separates the competitive ratios of RSA and the Symetric-RSA, two problems for which the bounds of Berman and Coulston is STOC 1997 were identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be viewed as the discrete counterparts (or a network counterpart) of RSA. For this second problem we present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points (the latter are similar to those we derived for RSA).