Balanced allocation on graphs
Krishnaram Kenthapadi, Rina Panigrahy · 2006
It is well known that if n balls are inserted into n bins, with high probability, the bin with maximum load contains (1 + o(1))log n / loglog n balls. Azar, Broder, Karlin, and Upfal [1] showed that instead of choosing one bin, if d ≥ 2 bins are chosen at random and the ball inserted into the least loaded of the d bins, the maximum load reduces drastically to log log n / log d+O(1). In this paper, we study the two choice balls and bins process when balls are not allowed to choose any two random bins, but only bins that are connected by an edge in an underlying graph. We show that for n balls and n bins, if the graph is almost regular with degree n ǫ, where ǫ is not too small, the previous bounds on the maximum load continue to hold. Precisely, the maximum load is