Answers are grounded in this paper and cite their sources.
We present a randomized on-line algorithm for the Metrical Tti System problem that achieves a competitive ratio of O(log6 n) for arbitrary metric spaces, against art oblivious adversary. This is the first algorithm to achieve a sublinear competitive ratio for all mernc spaces. Our algorithm uses a recent result of Bart.al[Bar96] thatan arbitrarymetric space can be probabilistically approximated by a set of metric spaces called "k-hierarchical well-separated trees" (k-HST'S). Indeed, the main technical result of this paper is an 0(}og2 n)-competitive algorithm for fl(log2 n)-HST spaces. This, combined with the result of [Bar96], yields the general bound.
No takes yet. Share an insight, caveat, or question.
Bartal et al. (1997) studied this question.