The Maximum Zero-Sum Partition problem

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...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1019; p. 114811
Main Authors: Fertin, Guillaume, Fontaine, Oscar, Jean, Géraldine, Vialette, Stéphane
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2024
Elsevier
Subjects:
Algorithmic complexity
Engineering Sciences
FPT
Inapproximability
Partition
Zero-sum
Algorithmic complexity
Partition
FPT
Zero-sum
Inapproximability
Zero-sum Partition Algorithmic complexity Inapproximability FPT
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114811