Distributed Approximation Algorithm for Resource Clustering

Olivier Beaumont, Nicolas Bonichon, Philippe Duchon, Hubert Larchevêque

Abstract: In this paper, we consider the clustering of resources on large scale platforms. More precisely, we target parallel applications consisting of independant tasks, where each task is to be processed on a different cluster. In this context, each cluster should be large enough so as to hold and process a task, and the maximal distance between two hosts belonging to the same cluster should be small in order to minimize latencies of intra-cluster communications. This corresponds to maximum bin covering with an extra distance constraint. We describe a distributed approximation algorithm that computes resource clustering with coordinates in ℚ in O(log2 n) steps and O(nlogn) messages, where n is the overall number of hosts. We prove that this algorithm provides an approximation ratio of $\frac{1}{3}$ .