Online matching in lossless expanders
Marius Zimand

TL;DR
This paper provides an explicit version of the online matching property of lossless expanders, enabling applications in dynamic set storage schemes and non-blocking network design.
Contribution
It presents a self-contained proof of an explicit online matching property for lossless expanders and demonstrates two practical applications.
Findings
Explicit online matching property for lossless expanders.
Construction of dynamic one-probe storage schemes using lossless expanders.
Application to non-blocking network design.
Abstract
Bauwens and Zimand [BZ 2019] have shown that lossless expanders have an interesting online matching property. The result appears in an implicit form in [BZ 2019]. We present an explicit version of this property which is directly amenable to typical applications, prove it in a self-contained manner that clarifies the role of some parameters, and give two applications. A lossless expander is a bipartite graph such that any subset of size at most of nodes on the left side of the bipartition has at least neighbors, where is the left degree.The main result is that any such graph, after a slight modification, admits online matching up to size . This means that for any sequence of nodes on the left side of the bipartition, one can assign in an online manner to each node in a set …
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Caching and Content Delivery · Cooperative Communication and Network Coding
