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 [17], and of Awerbuch, Kutten, and Peleg [15], in the context of data management and job scheduling. In these papers, as well as in other subsequent work [14, 4, 18] the cost of a distributed algorithm is compared to the cost of an optimal global-control algorithm. 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 [50]. We provide the first algorithms that allow processes to cooperate to finish their work in fewer steps. Specifically, we present two algorithms (with different strengths), and provide a competitive analysis for each one.