Maximizing Submodular Set Function With Connectivity Constraint: Theory and Application to Networks
نویسندگان
چکیده
منابع مشابه
Maximizing a Submodular Set Function
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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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 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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The concept of submodularity plays a vital role in combinatorial optimization. In particular, many important optimization problems can be cast as submodular maximization problems, including maximum coverage, maximum facility location and max cut in directed/undirected graphs. In this paper we present the first known approximation algorithms for the problem of maximizing a nondecreasing submodul...
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ژورنال
عنوان ژورنال: IEEE/ACM Transactions on Networking
سال: 2015
ISSN: 1063-6692,1558-2566
DOI: 10.1109/tnet.2014.2301816