Article Dans Une Revue Theoretical Computer Science Année : 2024

The Maximum Zero-Sum Partition problem

Oscar Fontaine
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Résumé

We study the Maximum Zero-Sum Partition problem (or MZSP), defined as follows: given a multiset S={a1,a2,…,an} of integers ai∈Z⁎ (where Z⁎ denotes the set of non-zero integers) such that ∑i=1nai=0, find a maximum cardinality partition {S1,S2,…,Sk} of S such that, for every 1≤i≤k, ∑aj∈Siaj=0. Solving MZSP is useful in genomics for computing evolutionary distances between pairs of species. Our contributions are a series of algorithmic results concerning MZSP, in terms of complexity, (in)approximability, with a particular focus on the fixed-parameter tractability of MZSP with respect to either (i) the size k of the solution, (ii) the number of negative (resp. positive) values in S and (iii) the largest integer in S.
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hal-04901397 , version 1 (20-01-2025)

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Guillaume Fertin, Oscar Fontaine, Géraldine Jean, Stéphane Vialette. The Maximum Zero-Sum Partition problem. Theoretical Computer Science, 2024, 1019, pp.114811. ⟨10.1016/j.tcs.2024.114811⟩. ⟨hal-04901397⟩
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