Stochastic Matching on Uniformly Sparse Graphs

Local Algorithms for Bounded Degree Sparsifiers in Sparse Graphs

“…This paper appeared in the proceedings of ITCS 2018 [55], and it triggered further work in the area. We next survey the most relevant follow-up papers [56,37,11,44].…”

“…Behnezhad et al [11] studied the stochastic matching problem, where one is given a graph G where each edge is realized independently with some constant probability p, and the goal is to find a constant degree subgraph of G whose expected realized matching size is close to that of G. This model of stochastic matching has received growing attention over the last few years due to its applications in kidney exchange and recommendation systems. [11] used the matching sparsifier presented in the current work for the stochastic setting.…”

“…Behnezhad et al [11] studied the stochastic matching problem, where one is given a graph G where each edge is realized independently with some constant probability p, and the goal is to find a constant degree subgraph of G whose expected realized matching size is close to that of G. This model of stochastic matching has received growing attention over the last few years due to its applications in kidney exchange and recommendation systems. [11] used the matching sparsifier presented in the current work for the stochastic setting. More specifically, the analysis of the current work carries over to the stochastic setting without any change if p = 1, and [11] showed that with few changes, the same analysis can be used to show that this matching sparsifier also works in the stochastic setting when p < 1.…”

“…[11] used the matching sparsifier presented in the current work for the stochastic setting. More specifically, the analysis of the current work carries over to the stochastic setting without any change if p = 1, and [11] showed that with few changes, the same analysis can be used to show that this matching sparsifier also works in the stochastic setting when p < 1.…”

Stochastic Vertex Cover with Few Queries

“…This stochastic setting has been studied extensively over the last two decades for various problems such as minimum spanning trees and matroids [14,15], packing problems [22], shortest paths [21], and most relevant to our work, matchings [9,10,2,3,8,22,5,1,7,6,4]. There has also been quite a lot of related work on "network reliability" in random subgraphs; see the book [11] for some classic results of the 1980's as well as [18,16] and the references therein for more recent works.…”