Abstract
We consider the linking set problem, which can be seen as a particular case of the multiple-choice knapsack problem. This problem occurs as a subproblem in a decomposition procedure for solving large-scale p-median problems such as the optimal diversity management problem. We show that if a non-increasing diference property of the costs in the linking set problem holds, then the problem can be solved by a greedy algorithm and the corresponding linear gap is null.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 63, Optimal Control, 2009.
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Agra, A., Requejo, C. The linking set problem: a polynomial special case of the multiple-choice knapsack problem. J Math Sci 161, 919–929 (2009). https://doi.org/10.1007/s10958-009-9612-y
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DOI: https://doi.org/10.1007/s10958-009-9612-y