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 Y. Bartal et al. (1992), and of B. Awerbuch et al. (1992), in the context of data management and job scheduling. In these papers, as well as in other subsequent sequent work, the cost of a distributed algorithm is compared to the cost of an optimal global-control algorithm. In this paper 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 M. Saks, N. Shavit, and H. Woll (1991). 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.