Maximizing a Monotone Submodular Function Subject to a Matroid Constraint

@article{Calinescu2011MaximizingAM,
  title={Maximizing a Monotone Submodular Function Subject to a Matroid Constraint},
  author={Gruia Calinescu and Chandra Chekuri and Martin P{\'a}l and Jan Vondr{\'a}k},
  journal={SIAM J. Comput.},
  year={2011},
  volume={40},
  pages={1740-1766}
}
Let f : 2 → R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2approximation [17] for this problem. For certain special cases, e.g. max|S|≤k f(S), the greedy algorithm yields a (1− 1/e)-approximation. It is known that this is optimal both in the value oracle model (where the only access to f is through a black box returning f(S) for a given set S) [37], and also for explicitly posed… CONTINUE READING
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