Carl Burch

FOCS Conference 1999 Conference Paper

Finely-Competitive Paging

• Avrim Blum
• Carl Burch
• Adam Tauman Kalai

We construct an online algorithm for paging that achieves an O(r+log k) competitive ratio when compared to an offline strategy that is allowed the additional ability to "rent" pages at a cost of 1/r. In contrast, the competitive ratio of the Marking algorithm for this scenario is O(r log k). Our algorithm can be thought of in the standard setting as having a "fine-grained" competitive ratio, achieving an O(1) ratio when the request sequence consists of a small number of working sets, gracefully decaying to O(log k) as this number increases. Our result is a generalization of the result by Y. Bartal et al. (1997) that one can achieve an O(r+log n) ratio for the unfair n-state uniform-space Metrical Task System problem. That result was a key component of the polylog(n) competitive randomized algorithm given in that paper for the general Metrical Task System problem. One motivation of this work is that it may be a first step toward achieving a polylog(k) randomized competitive ratio for the much more difficult k-server problem.

FOCS Conference 1998 Conference Paper

On Learning Monotone Boolean Functions

• Avrim Blum
• Carl Burch
• John Langford 0001

We consider the problem of learning monotone Boolean functions over {0, 1}/sup n/ under the uniform distribution. Specifically, given a polynomial number of uniform random samples for an unknown monotone Boolean function f, and given polynomial completing time, we would like to approximate f as well as possible. We describe a simple algorithm that we prove achieves error at most 1/2-/spl Omega/(1//spl radic/n), improving on the previous best bound of 1/2-/spl Omega/((log/sup 2/ n)/n). We also prove that no algorithm, given a polynomial number of samples, can guarantee error 1/2-/spl omega/((log n)//spl radic/n), improving on the previous best hardness bound of O(1//spl radic/n). These lower bounds hold even if the learning algorithm is allowed membership queries. Thus this paper settles to an O(log n) factor the question of the best achievable error for learning the class of monotone Boolean functions with respect to the uniform distribution.

STOC Conference 1997 Conference Paper

A polylog( n )-Competitive Algorithm for Metrical Task Systems

• Yair Bartal
• Avrim Blum
• Carl Burch
• Andrew Tomkins