We consider the community recovery problem on a multilayer variant of the hypergraph stochastic block model (HSBM). Each layer is associated with an independent realization of a d-uniform HSBM on N vertices. Given the similarity matrix containing the aggregated number of hyperedges incident to each pair of vertices, the goal is to obtain a partition of the N vertices into disjoint communities. In this work, we investigate a semidefinite programming (SDP) approach and obtain information-theoretic conditions on the model parameters that guarantee exact recovery both in the assortative and the disassortative cases.

翻译：我们考虑超图随机块模型（HSBM）多层变体上的社区恢复问题。每一层对应于一个在N个顶点上的d-均匀HSBM的独立实现。给定包含每对顶点关联超边聚合数量的相似矩阵，目标是将N个顶点划分为不相交的社区。在本研究中，我们探讨了半定规划（SDP）方法，并获得了模型参数的信息论条件，这些条件确保了在同配性和异配性两种情况下的精确恢复。