A Theory of Competitive Analysis for Distributed Algorithms

We introduce a theory of competitive analysis for distributed algorithms. The first steps in this direction were made in the seminal papers of Bartal, Fiat, and Rabani [18], and of Awerbuch, Kutten, and Peleg [16], in the context of data management and job scheduling. In these papers, as well as in other subsequent work [4, 15, 19, 14], the cost of a distributed algorithm is compared to the cost of an optimal global-control algorithm. (This is also done implicitly in the earlier work of Awerbuch and Peleg [17].) Here we introduce a more refined notion of competitiveness for distributed algorithms, one that reflects the performance of distributed algorithms more accurately. In particular, our theory allows one to compare the cost of a distributed on-line algorithm to the cost of an optimal distributed algorithm. We demonstrate our method by studying the cooperative collect primitive, first abstracted by Saks, Shavit, and Woll [57]. We present two algorithms (with different strengths) for this primitive, and provide a competitive analysis for each one. ∗A preliminary version of this paper was presented at the 35th Symposium on Foundations of Computer Science, November 1994. †IBM Almaden Research Center, 650 Harry Road, San Jose CA 95120. E-mail: [email protected], [email protected], resp. ‡Yale University, Department of Computer Science, 51 Prospect Street/P.O. Box 208285, New Haven CT 06520-8285. Supported by NSF grant CCR-9410228. Part of this research was performed while at IBM Almaden. E-mail: [email protected]. §Computer Science Division, U. C. Berkeley, CA 94720. Work supported in part by an NSF postdoctoral fellowship. During part of this research the fourth author was at IBM Almaden. E-Mail: [email protected]