Heuristics for the connected assignment problem in arrays

Given a set I of symbols, a set J of positions of an array, a gain value ρij for allocating i∈I to j∈J, the connected assignment problem in arrays (CAPA) is the problem consisting in finding an assignment of one symbol i to each position j so as to maximize the sum of the gains under the constraint...

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Bibliographic Details
Published inInternational transactions in operational research Vol. 28; no. 6; pp. 3147 - 3171
Main Authors Campêlo, Manoel, Soares, Joel C., Maciel, Tarcisio F., Lima, F. Rafael M.
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.11.2021
Subjects
Arrays
Assignment problem
Communication networks
connected assignment
heuristic
Integer programming
Linear programming
Operations research
radio resource allocation
Resource allocation
Symbols
Wireless communications
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Summary:Given a set I of symbols, a set J of positions of an array, a gain value ρij for allocating i∈I to j∈J, the connected assignment problem in arrays (CAPA) is the problem consisting in finding an assignment of one symbol i to each position j so as to maximize the sum of the gains under the constraint such that repeated symbols are adjacent in the array. CAPA has a direct application in radio resource allocation (RRA) in the uplink of the modern fourth‐generation (4G) wireless communication networks. We show that CAPA is NP‐hard. We present two integer linear programming formulations for CAPA and propose four heuristic solutions. They are compared using Monte Carlo simulations to generate instances compatible with a 4G system scenario as well as random instances based on a uniform distribution of the gains.
ISSN:0969-6016
1475-3995
DOI:10.1111/itor.12706