Barman, S and Krishna, A and Narahari, Y and Sadhukhan, S (2022) Nash Welfare Guarantees for Fair and Efficient Coverage. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2 - 15 December 2022, Troy, pp. 256-272.
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Abstract
We study coverage problems in which, for a set of agents and a given threshold T, the goal is to select T subsets (of the agents) that, while satisfying combinatorial constraints, achieve fair and efficient coverage among the agents. In this setting, the valuation of each agent is equated to the number of selected subsets that contain it, plus one. The current work utilizes the Nash social welfare function to quantify the extent of fairness and collective efficiency. We develop a polynomial-time (18 + o(1 ) ) -approximation algorithm for maximizing Nash social welfare in coverage instances. Our algorithm applies to all instances wherein, for the underlying combinatorial constraints, there exists an FPTAS for weight maximization. We complement the algorithmic result by proving that Nash social welfare maximization is APX-hard in coverage instances.
| Item Type: | Conference Paper |
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| Publication: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Combinatorial optimization; Constraint satisfaction problems; Polynomial approximation, 'current; Algorithmics; Coverage problem; Polynomial-time; Social welfare; Social welfare functions; Social welfare maximization, Approximation algorithms |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 01 Feb 2023 05:44 |
| Last Modified: | 01 Feb 2023 05:44 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79651 |
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