Elsevier

Information Processing Letters

Volume 48, Issue 4, 29 November 1993, Pages 177-182
Information Processing Letters

The competitiveness of randomized algorithms for on-line Steiner tree and on-line spanning tree problems

https://doi.org/10.1016/0020-0190(93)90142-VGet rights and content

Abstract

This paper considers a family of randomized on-line algorithms, Algorithm R(m), where 1 ⩽ m ⩽ n − 1 and n is the number of input points, for the on-line Steiner tree and on-line spanning tree problems on Euclidean space. Our main result is that if m is a fixed constant, the competitive ratios of Algorithm R(m) for the on-line Steiner tree and spanning tree problems are Θ(n). We also show that the competitive ratio of Algorithm R(n − 1), which is deterministic greedy algorithm, for the on-line spanning tree problem is the same as that for the on-line Steiner tree problem, which is O(log n).

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There are more references available in the full text version of this article.

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