We consider the problem of inferring a matching hidden in a weighted random k-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to the hidden matching or not. We show that for k > 2 and in the large-graph-size limit, an algorithmic first-order transition in the signal strength separates a regime in which a complete recovery of the hidden matching is feasible from a regime in which partial recovery is possible. This is in contrast to the k = 2 case, where the transition is known to be continuous. Finally, we consider the case of graphs presenting a mixture of edges and 3-hyperedges, interpolating between the k = 2 and the k = 3 cases, and we study how the transition changes from continuous to first order by tuning the relative amount of edges and hyperedges.

Urte Adomaityte, Anshul Toshniwal, Gabriele Sicuro, Lenka Zdeborová (2022). Planted matching problems on random hypergraphs. PHYSICAL REVIEW. E, 106(5), 1-12 [10.1103/PhysRevE.106.054302].

Planted matching problems on random hypergraphs

Gabriele Sicuro;
2022

Abstract

We consider the problem of inferring a matching hidden in a weighted random k-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to the hidden matching or not. We show that for k > 2 and in the large-graph-size limit, an algorithmic first-order transition in the signal strength separates a regime in which a complete recovery of the hidden matching is feasible from a regime in which partial recovery is possible. This is in contrast to the k = 2 case, where the transition is known to be continuous. Finally, we consider the case of graphs presenting a mixture of edges and 3-hyperedges, interpolating between the k = 2 and the k = 3 cases, and we study how the transition changes from continuous to first order by tuning the relative amount of edges and hyperedges.
2022
Urte Adomaityte, Anshul Toshniwal, Gabriele Sicuro, Lenka Zdeborová (2022). Planted matching problems on random hypergraphs. PHYSICAL REVIEW. E, 106(5), 1-12 [10.1103/PhysRevE.106.054302].
Urte Adomaityte; Anshul Toshniwal; Gabriele Sicuro; Lenka Zdeborová
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/958337
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