The Stochastic Matching Problem
Sepehr Assadi, Sanjeev Khanna, Yang Li · 2017
In the stochastic matching problem, we are given a general (not necessarily bipartite) graph G(V,E), where each edge in E is realized with some constant probability p > 0 and the goal is to compute a bounded-degree (bounded by a function depending only on p) subgraph H of G such that the expected maximum matching size in H is close to the expected maximum matching size in G. The algorithms in this setting are considered non-adaptive as they have to choose the subgraph H without knowing any information about the set of realized edges in G. Originally motivated by an application to kidney exchange, the stochastic matching problem and its variants have received significant attention in recent years.