This paper provides a systematic study of several recently suggested 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 how these measures evaluate the Greedy Algorithm and Lazy Double Coverage, commonly studied algorithms in the context of server problems. We examine Competitive Analysis, the Max/Max Ratio, the Random Order Ratio, Bijective Analysis and Relative Worst Order Analysis and determine how they compare the two algorithms. We find that by the Max/Max Ratio and Bijective Analysis, Greedy is the better algorithm. Under the other measures Lazy Double Coverage is better, though Relative Worst Order Analysis indicates that Greedy is sometimes better. Our results also provide the first proof of optimality of an algorithm under Relative Worst Order Analysis.
Lecture Notes in Computer Science: 11th International Symposium, Wads 2009, Banff, Canada, August 21-23, 2009. Proceedings, 2009, p. 119-130