On maximizing a monotone k-submodular function subject to a matroid constraint
نویسندگان
چکیده
منابع مشابه
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
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 [14] 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...
متن کاملOn maximizing a monotone k-submodular function subject to a matroid constraint
A k-submodular function is an extension of a submodular function in that its input is given by k disjoint subsets instead of a single subset. For unconstrained nonnegative ksubmodular maximization, Ward and Živný proposed a constant-factor approximation algorithm, which was improved by the recent work of Iwata, Tanigawa and Yoshida presenting a 1/2-approximation algorithm. Iwata et al. also pro...
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In this work we present the first practical ( 1 e − ǫ ) -approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the decreasing-threshold procedure of Badanidiyuru and Vondrak (SODA 2014) with a smoother version of the measured continuous greedy algorithm of Feldman et al. (FOCS 2011). This enables us to...
متن کاملMaximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
Let f : 2 → R be a non-decreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It is known that the greedy algorithm yields a 1/2-approximation [9] for this problem. It is also known, via a reduction from the max-k-cover problem, that there is no (1− 1/e+ )-approximation for any constant > 0, unless P = NP [6]. In this paper, we improve the 1/2-appr...
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Maximizing a monotone submodular function subject to a b-matching constraint is increasing in importance due to the application for the content spread maximization problem, but few practical algorithms are known other than the greedy algorithm. The best approximation scheme so far is the local search algorithm, proposed by Feldman, Naor, Schwartz, Ward (2011). It obtains a 1/(2+ 1 k +ε)-approxi...
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ژورنال
عنوان ژورنال: Discrete Optimization
سال: 2017
ISSN: 1572-5286
DOI: 10.1016/j.disopt.2017.01.003