Decentralized algorithms using both local and random probes for P2P load balancing

• Authors: Krishnaram Kenthapadi;Gurmeet Singh Manku
• Venue: Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
• Year: 2005

We study randomized algorithms for placing a sequence ofn nodes on a circle with unit perimeter. Nodes divide thecircle into disjoint arcs. We desire that a newly-arrived node(which is oblivious of its index in the sequence) choose itsposition on the circle by learning the positions of as few existingnodes as possible. At the same time, we desire that that thevariation in arc-lengths be small. To this end, we propose a newalgorithm that works as follows: The kth nodechooses r random points on the circle, inspects the sizes ofv arcs in the vicinity of each random point, and placesitself at the mid-point of the largest arc encountered. We showthat for any combination of r and v satisfyingrv ¡Ý c log k, where c isa small constant, the ratio of the largest to the smallestarc-length is at most eight w.h.p., for an arbitrarily longsequence of n nodes. This strategy of node placementunderlies a novel decentralized load-balancing algorithm that wepropose for Distributed Hash Tables (DHTs) in peer-to-peerenvironments.Underlying the analysis of our algorithm is StructuredCoupon Collection over n/b disjointcliques with b nodes per clique, for anyn, b ≥ 1. Nodes areinitially uncovered. At each step, we choose dnodes independently and uniformly at random. If all the nodes inthe corresponding cliques are covered, we do nothing. Otherwise,from among the chosen cliques with at least one uncovered node, weselect one at random and cover an uncovered node within thatclique. We show that as long as bd ≥c log n,O(n) steps are sufficient tocover all nodes w.h.p. and each of the firstΩ(n) steps succeeds in covering a nodew.h.p. These results are then utilized to analyze a stochasticprocess for growing binary trees that are highly balanced -- theleaves of the tree belong to at most four different levels withhigh probability.