Perfectly Balanced AllocationWith Estimated Average Using Approximately Constant Retries

Balanced allocation of online balls-and-bins has long been an active area of research for efficient load balancing and hashing applications. There exists a large number of results in this domain with different settings, such as parallel allocations [1], multi-dimensional allocations [5], weighted balls [4] etc. For sequential multi-choice allocation where m balls are thrown into n bins with each ball choosing d (constant) bins independently uniformly at random, the maximum load of a bin is O(log log n)+m=n with high probability [3]. This offers the current best known allocation scheme. However, for d = (log n), the gap obtained is of O(1) [9]. A similar constant gap bound has been established for parallel allocations with O(log n) communication rounds [12].
In this paper we propose a novel multi-choice allocation algorithm, Improved D-choice with Estimated Average (IDEA) achieving a constant gap with high probability for the sequential single-dimensional online allocation problem with constant d. We achieve a maximum load of dm=ne with high probability for constant d choice scheme with approximately constant number of retries or rounds per ball. We also show that the bound holds even for an arbitrary large number of balls, m >> n. Further, we generalize
this result to the weighted case, where the balls have weights drawn from an arbitrary weight distribution with finite variance. We show that the gap in this case is also independent of the number of balls thrown and is a constant. We also propose that IDEA provides constant gap bound w.h.p. in the multi-dimensional scenario for m = n.

By: Sourav Dutta, Souvik Bhattacherjee, Ankur Narang

Published in: RI11023 in 2011


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