5,755 research outputs found
Ramsey-type theorems for metric spaces with applications to online problems
A nearly logarithmic lower bound on the randomized competitive ratio for the
metrical task systems problem is presented. This implies a similar lower bound
for the extensively studied k-server problem. The proof is based on Ramsey-type
theorems for metric spaces, that state that every metric space contains a large
subspace which is approximately a hierarchically well-separated tree (and in
particular an ultrametric). These Ramsey-type theorems may be of independent
interest.Comment: Fix an error in the metadata. 31 pages, 0 figures. Preliminary
version in FOCS '01. To be published in J. Comput. System Sc
Using genetic algorithms to create meaningful poetic text
Work carried out when all authors were at the University of Edinburgh.Peer reviewedPostprin
Randomized online computation with high probability guarantees
We study the relationship between the competitive ratio and the tail
distribution of randomized online minimization problems. To this end, we define
a broad class of online problems that includes some of the well-studied
problems like paging, k-server and metrical task systems on finite metrics, and
show that for these problems it is possible to obtain, given an algorithm with
constant expected competitive ratio, another algorithm that achieves the same
solution quality up to an arbitrarily small constant error a with high
probability; the "high probability" statement is in terms of the optimal cost.
Furthermore, we show that our assumptions are tight in the sense that removing
any of them allows for a counterexample to the theorem. In addition, there are
examples of other problems not covered by our definition, where similar high
probability results can be obtained.Comment: 20 pages, 2 figure
- ā¦