Linear bounds for on-line Steiner problems
Information Processing Letters
Competitive algorithms for distributed data management
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Multicast tree generation in networks with asymmetric links
IEEE/ACM Transactions on Networking (TON)
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
On-line algorithms for Steiner tree problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved bounds for the online steiner tree problem in graphs of bounded edge-asymmetry
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A Near-Tight Bound for the Online Steiner Tree Problem in Graphs of Bounded Asymmetry
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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This paper addresses the competitiveness of online algorithms for two Steiner Tree problems. In the first problem, the underlying graph is directed and has bounded asymmetry, namely the maximum weight of antiparallel links in the graph does not exceed a parameter α. Previous work on this problem has left a gap on the competitive ratio which is as large as logarithmic in k. We present a refined analysis, both in terms of the upper and the lower bounds, that closes the gap and shows that a greedy algorithm is optimal for all values of the parameter α. The second part of the paper addresses the Euclidean Steiner tree problem on the plane. Alon and Azar [SoCG 1992, Disc. Comp. Geom. 1993] gave an elegant lower bound on the competitive ratio of any deterministic algorithm equal to Ω(logk/ loglogk); however, the best known upper bound is the trivial bound O(logk). We give the first analysis that makes progress towards closing this long-standing gap. In particular, we present an online algorithm with competitive ratio O(logk/ loglogk), provided that the optimal offline Steiner tree belongs in a class of trees with relatively simple structure. This class comprises not only the adversarial instances of Alon and Azar, but also all rectilinear Steiner trees which can be decomposed in a polylogarithmic number of rectilinear full Steiner trees.