Double hashing thresholds via local weak convergence

  • Mathieu Leconte
  • Published 2013 in
    2013 51st Annual Allerton Conference on…

Abstract

A lot of interest has recently arisen in the analysis of multiple-choice “cuckoo hashing” schemes. In this context, a main performance criterion is the load threshold under which the hashing scheme is able to build a valid hashtable with high probability in the limit of large systems; various techniques have successfully been used to answer this question (differential equations, combinatorics, cavity method) for increasing levels of generality of the model. However, the hashing scheme analysed so far is quite utopic in that it requires to generate a lot of independent, fully random choices. Schemes with reduced randomness exists, such as “double hashing”, which is expected to provide similar asymptotic results as the ideal scheme, yet they have been more resistant to analysis so far. In this paper, we point out that the approach via the cavity method extends quite naturally to the analysis of double hashing and allows to compute the corresponding threshold. The path followed is to show that the graph induced by the double hashing scheme has the same local weak limit as the one obtained with full randomness.

DOI: 10.1109/Allerton.2013.6736515

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Cite this paper

@article{Leconte2013DoubleHT, title={Double hashing thresholds via local weak convergence}, author={Mathieu Leconte}, journal={2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)}, year={2013}, pages={131-137} }