The Performance of greedy algorithms for the on-line steiner tree and related problems

Abstract

We study the on-line Steiner tree problem on a general metric space. We show that the greedy on-line algorithm isO(log((d/z)s))-competitive, wheres is the number of regular nodes,d is the maximum metric distance between any two revealed nodes, andz is the optimal off-line cost. Our results refine the previous known bound [9] and show that AlgorithmSB of Bartalet al. [3] for the on-line file allocation problem isO(log logN)-competitive on anN-node hypercube or butterfly network. A lower bound of Ω(log((d/z)s)) is shown to hold.