 
Summary: Online Algorithms
Susanne Albers Stefano Leonardiy
Over the past twelve years, onlinealgorithms have received considerableresearch interest. Online
problems had been investigated already in the seventies and early eighties but an extensive,
systematic study started only when Sleator and Tarjan 41] suggested comparing an online
algorithm to an optimal o ine algorithm and Karlin, Manasse, Rudolph and Sleator 29] coined
the term competitive analysis.
Foundations
An online algorithm receives the input incrementally, one piece at a time. In response to each
input portion, the algorithm must generate output, not knowing future input. In a competitive
analysis an online algorithm A is compared to an optimal o ine algorithm OPT. An optimal
o ine algorithm knows the entire input sequence in advance and can process it optimally.
Given an input sequence I, let CA(I) and COPT(I) denote the costs incurred by A and OPT
in processing I. Algorithm A is called ccompetitive if there exists a constant a such that
CA(I) c COPT(I) + a, for all input sequences I. An analogous de nition can be given for
online maximization problems. We note that a competitive algorithm must perform well on all
input sequences.
In the above de nition it is assumed that A is a deterministic algorithm. Randomization often
allows online algorithms to obtain better competitive ratios than deterministic algorithms. Ben
David et al. 13] explored the power of randomization in online algorithms. Given a randomized
