Constrained submodular maximization via greedy local search
We present a simple combinatorial 1−e−22-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is known to be hard to approximate within factor better than 1−1∕e. We extend the algorithm to yield 1−e−(k+1)k+1 approx...
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| Vydané v: | Operations research letters Ročník 47; číslo 1; s. 1 - 6 |
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Elsevier B.V
01.01.2019
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| Abstract | We present a simple combinatorial 1−e−22-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is known to be hard to approximate within factor better than 1−1∕e. We extend the algorithm to yield 1−e−(k+1)k+1 approximation for submodular maximization subject to a single knapsack and k matroid constraints, for any fixed k>1.
Our algorithms, which combine the greedy algorithm of Khuller et al. (1999) and Sviridenko (2004) with local search, show the power of this natural framework in submodular maximization with combined constraints. |
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| AbstractList | We present a simple combinatorial 1−e−22-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is known to be hard to approximate within factor better than 1−1∕e. We extend the algorithm to yield 1−e−(k+1)k+1 approximation for submodular maximization subject to a single knapsack and k matroid constraints, for any fixed k>1.
Our algorithms, which combine the greedy algorithm of Khuller et al. (1999) and Sviridenko (2004) with local search, show the power of this natural framework in submodular maximization with combined constraints. |
| Author | Sarpatwar, Kanthi K. Shachnai, Hadas Schieber, Baruch |
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| Cites_doi | 10.1145/285055.285059 10.1287/moor.3.3.177 10.1007/BFb0121195 10.1137/110839655 10.1061/(ASCE)0733-9496(2008)134:6(516) 10.1007/BF01588971 10.1137/090750020 10.1137/080733991 10.1287/moor.7.3.410 10.1007/s00037-006-0205-6 10.1016/S0167-6377(03)00062-2 10.1145/2746226 10.1016/S0020-0190(99)00031-9 |
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