Bipartite Random Graphs and Cuckoo Hashing
نویسنده
چکیده
The aim of this paper is to extend the analysis of Cuckoo Hashing of Devroye and Morin in 2003. In particular we make several asymptotic results much more precise. We show, that the probability that the construction of a hash table succeeds, is asymptotically 1 − c(ε)/m + O(1/m) for some explicit c(ε), where m denotes the size of each of the two tables, n = m(1 − ε) is the number of keys and ε ∈ (0, 1). The analysis rests on a generating function approach to the so called Cuckoo Graph, a random bipartite graph. We apply a double saddle point method to obtain asymptotic results covering tree sizes, the number of cycles and the probability that no complex component occurs.
منابع مشابه
Maximum Matchings in Random Bipartite Graphs and the Space Utilization of Cuckoo Hashtables
We study the the following question in Random Graphs. We are given two disjoint sets L,R with |L| = n = αm and |R| = m. We construct a random graph G by allowing each x ∈ L to choose d random neighbours in R. The question discussed is as to the size μ(G) of the largest matching in G. When considered in the context of Cuckoo Hashing, one key question is as to when is μ(G) = n whp? We answer this...
متن کاملA Faster Algorithm for Cuckoo Insertion and Bipartite Matching in Large Graphs
Hash tables are ubiquitous in computer science for efficient access to large datasets. However, there is always a need for approaches that offer compact memory utilisation without substantial degradation of lookup performance. Cuckoo hashing is an efficient technique of creating hash tables with high space utilisation and offer a guaranteed constant access time. We are given n locations and m i...
متن کاملConvergence of multivariate belief propagation, with applications to cuckoo hashing and load balancing
This paper is motivated by two applications, namely i) generalizations of cuckoo hashing,a computationally simple approach to assigning keys to objects, and ii) load balancing incontent distribution networks, where one is interested in determining the impact of contentreplication on performance. These two problems admit a common abstraction: in bothscenarios, performance is char...
متن کاملMaximum Bipartite Matching Size And Application to Cuckoo Hashing
Cuckoo hashing with a stash is a robust multiplechoice hashing scheme with high memory utilization that canbe used in many network device applications. Unfortunately, formemory loads beyond 0.5, little is known on its performance.In this paper, we analyze its average performance over suchloads. We tackle this problem by recasting the problem as ananalysis of the expected...
متن کاملAnalysing the Performance of GPU Hash Tables for State Space Exploration
In the past few years, General Purpose Graphics Processors (GPUs) have been used to significantly speed up numerous applications. One of the areas in which GPUs have recently led to a significant speed-up is model checking. In model checking, state spaces, i.e., large directed graphs, are explored to verify whether models satisfy desirable properties. GPUEXPLORE is a GPU-based model checker tha...
متن کامل