A Comparison of Performance Measures for Online Algorithms
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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.
KeywordsOnline algorithms K-server problem Performance measures
The first and third author were supported in part by the Danish Council for Independent Research, Natural Sciences. Part of this work was carried out while these authors were visiting the University of California, Irvine, and the University of Waterloo, Canada. The second author was supported in part by NSF Grants CCR-0514082 and CCF-0916181. The authors would like to thank Christian Kudahl for calling their attention to two oversights in a previous version of this paper, one in the definition of the lazy version of an algorithm, and another in the modified definition of the Random Order Ratio.
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