# Tight Bounds for Double Coverage Against Weak Adversaries

Tight Bounds for Double Coverage Against Weak Adversaries We study the Double Coverage (DC) algorithm for the k-server problem in tree metrics in the (h, k)-setting, i.e., when DC with k servers is compared against an offline optimum algorithm with h ≤ k servers. It is well-known that in such metric spaces DC is k-competitive (and thus optimal) for h = k. We prove that even if k > h the competitive ratio of DC does not improve; in fact, it increases slightly as k grows, tending to h + 1. Specifically, we give matching upper and lower bounds of k ( h + 1 ) k + 1 $\frac {k(h+1)}{k+1}$ on the competitive ratio of DC on any tree metric. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theory of Computing Systems Springer Journals

# Tight Bounds for Double Coverage Against Weak Adversaries

, Volume 62 (2) – Sep 2, 2016
17 pages

Publisher
Springer Journals
Subject
Computer Science; Theory of Computation
ISSN
1432-4350
eISSN
1433-0490
D.O.I.
10.1007/s00224-016-9703-3
Publisher site
See Article on Publisher Site

### Abstract

We study the Double Coverage (DC) algorithm for the k-server problem in tree metrics in the (h, k)-setting, i.e., when DC with k servers is compared against an offline optimum algorithm with h ≤ k servers. It is well-known that in such metric spaces DC is k-competitive (and thus optimal) for h = k. We prove that even if k > h the competitive ratio of DC does not improve; in fact, it increases slightly as k grows, tending to h + 1. Specifically, we give matching upper and lower bounds of k ( h + 1 ) k + 1 $\frac {k(h+1)}{k+1}$ on the competitive ratio of DC on any tree metric.

### Journal

Theory of Computing SystemsSpringer Journals

Published: Sep 2, 2016

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