A simple deterministic algorithm for symmetric submodular maximization subject to a knapsack constraint
We obtain a polynomial-time deterministic (2ee−1+ϵ)-approximation algorithm for maximizing symmetric submodular functions under a budget constraint. Although there exist randomized algorithms with better expected performance, our algorithm achieves the best known factor achieved by a deterministic a...
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| Vydáno v: | Information processing letters Ročník 163; s. 106010 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.11.2020
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| Témata: | |
| ISSN: | 0020-0190, 1872-6119 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We obtain a polynomial-time deterministic (2ee−1+ϵ)-approximation algorithm for maximizing symmetric submodular functions under a budget constraint. Although there exist randomized algorithms with better expected performance, our algorithm achieves the best known factor achieved by a deterministic algorithm, improving on the previously known factor of 6. Furthermore, it is simple, combining two elegant algorithms for related problems; the local search algorithm of Feige, Mirrokni and Vondrák [1] for unconstrained submodular maximization, and the greedy algorithm of Sviridenko [2] for non-decreasing submodular maximization subject to a knapsack constraint.
•We study symmetric submodular maximization subject to a knapsack constraint.•Submodular functions become monotone when restricted to their local maxima.•They are “almost” monotone on their approximate local maxima.•There is a greedy approach that is robust under small deviations from monotonicity.•There is a 2e/(e−1)-approximation algorithm for symmetric submodular objectives. |
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| ISSN: | 0020-0190 1872-6119 |
| DOI: | 10.1016/j.ipl.2020.106010 |