A local algorithm and its percolation analysis of bipartite z-matching problem

Abstract A z -matching on a bipartite graph is set of edges, among which each vertex two types the adjacent to at most 1 and ( ⩾ 1 ) respectively. The problem concerns finding -matchings with maximum size. Our approach this combinatorial optimization twofold. From an algorithmic perspective, we adopt local algorithm as linear approximate solver find any instance, whose basic component generalized greedy leaf removal procedure in theory. theoretical uncorrelated random graphs, develop mean-field theory for percolation phenomenon underlying algorithm, leading analytical estimation sizes graphs. corrects prediction by belief propagation zero-temperature limit (Kreačić Bianconi 2019 Europhys. Lett. 126 028001). Besides, our framework extends core analysis k -XORSAT problems general context hypergraphs arbitrary degree distributions factor variable nodes.