Notice
Online matching for the multiclass Stochastic Block Model
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Descriptif
A matching in a graph is a set of edges that do not share endpoints. Developing algorithms that find large matchings is an important problem. An algorithm is said to be online if it has to construct the matching step by step as the graph is "discovered". Online algorithms have received a lot of attention in recent years due to their wide applicability (job markets, internet advertisements, etc.). We study online algorithms in the Stochastic Block Model (SBM), a classical random graph model in which vertices have classes, and two vertices are adjacent or not according to a probability that depends on the classes involved. We study the dense case, i.e., where the adjacency probabilities do not scale with the size of the graph. In this context, we show that there is a phase transition in the performance of online algorithms governed by a condition, called NCOND in the literature, that depends on the adjacency probabilities of the SBM.
This is a joint work with Matthieu Jonckheere and Pascal Moyal.
Thème
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