 
Summary: Chapter 1
Online Choice of Online Algorithms
Yossi Azar \Lambda Andrei Z. Broder \Lambda Mark S. Manasse \Lambda
Abstract
Let fA1 ; A2 ; : : : ; Amg be a set of online algorithms for
a problem P with input set I. We assume that P can
be represented as a metrical task system. Each A i has
a competitive ratio a i with respect to the optimum off
line algorithm, but only for a subset of the possible inputs
such that the union of these subsets covers I. Given this
setup, we construct a generic deterministic online algorithm
and a generic randomized online algorithm for P that are
competitive over all possible inputs. We show that their
competitive ratios are optimal up to constant factors. Our
analysis proceeds via an amusing card game.
1 Introduction
A common trick of the trade in algorithm design is to
combine several algorithms using round robin execution.
The basic idea is that, given a set of m algorithms
for a problem P , one can simulate them one at a
