- A Comparison of Performance Measures for Online Algorithms.
- Joan Boyar, Sandy Irani, and Kim S. Larsen.
Algorithmica. Accepted for publication.
This paper provides a systematic study of several proposed
measures for online algorithms in the context of a specific problem,
namely, the two server problem on three colinear points.
Even though the problem is simple, it encapsulates a core challenge in
online algorithms which is to balance greediness and adaptability.
We examine Competitive Analysis, the Max/Max Ratio, the Random Order Ratio,
Bijective Analysis and Relative Worst Order Analysis, and determine
how these measures compare the Greedy Algorithm, Double Coverage,
and Lazy Double Coverage,
commonly studied algorithms in the context of server problems.
We find that by the Max/Max Ratio and Bijective Analysis, Greedy is the
best of the three algorithms. Under the other measures, Double Coverage and
Lazy Double Coverage are
better, though Relative Worst Order Analysis indicates
that Greedy is sometimes better.
Only Bijective Analysis and Relative Worst Order Analysis indicate that
Lazy Double Coverage is better than Double Coverage.
Our results also provide the first
proof of optimality of an algorithm under Relative Worst Order Analysis.
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