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Computing a many-to-many matching with demands and capacities between two sets using the Hungarian algorithm (2211.01612v1)
Published 3 Nov 2022 in cs.DS
Abstract: Given two sets A={a_1,a_2,...,a_s} and {b_1,b_2,...,b_t}, a many-to-many matching with demands and capacities (MMDC) between A and B matches each element a_i in A to at least \alpha_i and at most \alpha'_i elements in B, and each element b_j in B to at least \beta_j and at most \beta'_j elements in A for all 1=<i<=s and 1=<j<=t. In this paper, we present an algorithm for finding a minimum-cost MMDC between A and B using the well-known Hungarian algorithm.