Results 1 - 10 of 251

A Tight Combinatorial Algorithm for Submodular Maximization Subject to a Matroid Constraint

by Yuval Filmus, Justin Ward , 2012
"... We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is extremely simple and requires no rounding. It consists of the g ..."
Abstract - Cited by 11 (2 self) - Add to MetaCart
We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is extremely simple and requires no rounding. It consists

Online submodular maximization under a matroid constraint . . .

by Daniel Golovin, Andreas Krause, et al. , 2014
"... Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy decreases the marginal utility of each ad or information source ..."
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source. We show that these and other problems can be formalized as repeatedly selecting an assignment of items to positions to maximize a sequence of monotone submodular functions that arrive one by one. We present an efficient algorithm for this general problem and analyze it in the no-regret model. Our

Maximizing a Monotone Submodular Function subject to a Matroid Constraint

by Gruia Calinescu , Chandra Chekuri, Martin Pal, Jan Vondrak , 2008
"... Let f: 2 X → 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 1/2 approximation [14] for this problem. For certain special cases, e.g. max |S|≤k f(S), the greedy algorithm yields a (1 − 1/e)-app ..."
Abstract - Cited by 62 (0 self) - Add to MetaCart
Let f: 2 X → 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 1/2 approximation [14] for this problem. For certain special cases, e.g. max |S|≤k f(S), the greedy algorithm yields a (1 − 1/e

Fast algorithms for maximizing submodular functions

by Ashwinkumar Badanidiyuru - In SODA , 2014
"... There has been much progress recently on improved approximations for problems involving submodular ob-jective functions, and many interesting techniques have been developed. However, the resulting algorithms are often slow and impractical. In this paper we develop algorithms that match the best know ..."
Abstract - Cited by 13 (3 self) - Add to MetaCart
known approximation guarantees, but with significantly improved running times, for maximizing a monotone submodular function f: 2[n] → R+ subject to various constraints. As in pre-vious work, we measure the number of oracle calls to the objective function which is the dominating term in the running

Near-optimal sensor placements in gaussian processes

by Andreas Krause, Ajit Singh, Carlos Guestrin, Chris Williams - In ICML , 2005
"... When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy (variance) in t ..."
Abstract - Cited by 342 (34 self) - Add to MetaCart
information is NP-complete. To address this issue, we describe a polynomial-time approximation that is within (1 − 1/e) of the optimum by exploiting the submodularity of mutual information. We also show how submodularity can be used to obtain online bounds, and design branch and bound search procedures. We

Maximizing a Submodular Set Function subject to a Matroid Constraint (Extended Abstract)

by Gruia Calinescu, Chandra Chekuri, Martin Pál, Jan Vondrák - PROC. OF 12 TH IPCO , 2007
"... Let f: 2 N → 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 ..."
Abstract - Cited by 112 (14 self) - Add to MetaCart
Let f: 2 N → 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

Non-monotone submodular maximization under matroid and knapsack constraints

by Jon Lee, Vahab S. Mirrokni, Viswanath Nagarajan, Maxim Sviridenko - In Proc. 41th ACM Symp. on Theory of Computing , 2009
"... Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Un ..."
Abstract - Cited by 40 (1 self) - Add to MetaCart
-monotone submodular functions. In particular, for any constant k, we present a 1 k+2+ 1 k +ǫ-approximation for the submodular maximization problem under k matroid constraints, 1 k+ǫ and a ( 1 5 − ǫ)-approximation algorithm for this problem subject to k knapsack constraints (ǫ> 0 is 1 any constant). We improve

Submodular Stochastic Probing on Matroids

by Marek Adamczyk, Maxim Sviridenko, Justin Ward
"... In a stochastic probing problem we are given a universe E, where each element e ∈ E is active independently with probability pe ∈ [0, 1], and only a probe of e can tell us whether it is active or not. On this universe we execute a process that one by one probes elements — if a probed element is acti ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
submodular objective function. We give a (1 − 1/e)/(kin + kout + 1)-approximation algorithm for the case in which we are given kin ≥ 0 matroids as inner constraints and kout ≥ 1 matroids as outer constraints. There are two main ingredients behind this result. First is a previously unpublished stronger bound

Adaptive submodular optimization under matroid constraints

by Daniel Golovin, Andreas Krause , 2011
"... Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this article, we extend this classic result to a general class of ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this article, we extend this classic result to a general class

Submodular Maximization Over Multiple Matroids via Generalized Exchange Properties

by Jon Lee, Maxim Sviridenko, Jan Vondrák , 2009
"... Submodular-function maximization is a central problem in combinatorial optimization, generalizing many important NP-hard problems including Max Cut in digraphs, graphs and hypergraphs, certain constraint satisfaction problems, maximum-entropy sampling, and maximum facility-location problems. Our mai ..."
Abstract - Cited by 44 (8 self) - Add to MetaCart
and Fisher, obtained more than 30 years ago. Also, our analysis can be applied to the problem of maximizing a linear objective function and even a general non-monotone submodular function subject to k matroid constraints. We show that in these cases the approximation guarantees of our algorithms are 1/(k − 1
Results 1 - 10 of 251