A Space Efficient Algorithm for Multiset Multicover with Multiplicity Constraints Problem via Algebraic Method

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Pu Wu, Huiqin Jiang, Zehui Shao, Jin Xu

Published: 2024, Last Modified: 15 Jan 2026COCOON (2) 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Given a set S with n elements and a collection \(\mathcal {F}\) of multisets over S, the multiset multicover with multiplicity constraints problem (MSMC-MCP) entails finding the minimum number of multisets from \(\mathcal {F}\) required to cover each element \(s_i \in S\) at least specified \(b_i\) times, while ensuring that each multiset \(F_i \in \mathcal {F}\) can be selected no more than specified \(d_i\) times. Here, \(b = \max _{1\le i\le n} b_i\). MSMC-MCP is a generalization of classic set cover problem.