Maximum Bipartite Matching Size And Application to Cuckoo Hashing
Cached
Download Links
BibTeX
@MISC{Kanizo_maximumbipartite,
author = {Yossi Kanizo and David Hay and Isaac Keslassy},
title = {Maximum Bipartite Matching Size And Application to Cuckoo Hashing },
year = {}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Cuckoo hashing with a stash is a robust high-performance hashing scheme that can be used in many real-life applications. It complements cuckoo hashing by adding a small stash storing the elements that cannot fit into the main hash table due to collisions. However, the exact required size of the stash and the tradeoff between its size and the memory over-provisioning of the hash table are still unknown. We settle this question by investigating the equivalent maximum matching size of a random bipartite graph, with a constant left-side vertex degree d = 2. Specifically, we provide an exact expression for the expected maximum matching size and show that its actual size is close to its mean, with high probability. This result relies on decomposing the bipartite graph into connected components, and then separately evaluating the distribution of the matching size in each of these components. In particular, we provide an exact expression for any finite bipartite graph size and also deduce asymptotic results as the number of vertices goes to infinity. We also extend our analysis to cases where only part of the left-side vertices have a degree of 2; as well as to the case where the set of right-size vertices is partitioned into two subsets, and each
Citations
No citations identified.
