随机二部图的最大匹配与Cuckoo哈希表的空间利用
Maximum Matchings in Random Bipartite Graphs and the Space Utilization of Cuckoo Hashtables
摘要：
我们在随机图中研究以下问题。我们给出了两个不相交集$L,R$与$|L|=n=αm$和$|R|=m$。我们通过允许每个$x\in L$在$R$中选择$d$随机邻居来构造随机图$G$。讨论的问题是关于$G$中最大匹配的大小$μ(G)$。当在布谷鸟散列的上下文中考虑时，一个关键问题是$μ(G)=n$何时是whp？当$d$至少为4时，我们精确地回答这个问题。我们还建立了一个精确的阈值时，阶段1的Karp-Sipser贪婪匹配算法足以计算最大匹配的whp。
英文摘要：
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 $x\in L$ 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 question exactly when $d$ is at least four. We also establish a precise threshold for when Phase 1 of the Karp-Sipser Greedy matching algorithm suffices to compute a maximum matching whp.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
