摘要
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). © 1993.