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Approximations for Monotone and Non-monotone Submodular Maximization with Knapsack Constraints [article]

Ariel Kulik, Hadas Shachnai, Tami Tamir
2011 arXiv   pre-print
In this paper we consider the problem of maximizing any submodular function subject to d knapsack constraints, where d is a fixed constant.  ...  We use this relation to improve the best known approximation ratio for the problem to 1/4- , for any > 0, and to obtain a nearly optimal (1-e^-1-)-approximation ratio for the monotone case, for any >0.  ...  In [2] , Bansal et al. studied the problem of maximizing a monotone submodular function subject to n knapsack constraints, for arbitrary n ≥ 1, where each element appears in up to k constraints, and k  ... 
arXiv:1101.2940v1 fatcat:5ie2mkgsxng3xid6hv4g6l7vqa

Maximizing Non-monotone Submodular Set Functions Subject to Different Constraints: Combined Algorithms [article]

Salman Fadaei, MohammadAmin Fazli, MohammadAli Safari
2016 arXiv   pre-print
This implies a 0.13-approximation for several discrete problems, such as maximizing a non-negative submodular function subject to a matroid constraint and/or multiple knapsack constraints.  ...  We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity  ...  The first author is also thankful to Ali Moeini (his M.Sc. advisor), Dara Moazzami, and Jasem Fadaei for their help and advice.  ... 
arXiv:1101.2973v5 fatcat:sjubtewxpbaqzhb4vchzbf5kve

Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the Fly [article]

Baharan Mirzasoleiman, Stefanie Jegelka, Andreas Krause
2017 arXiv   pre-print
of independence systems I, provides a constant 1/(1+2/√(α)+1/α +2d(1+√(α))) approximation guarantee for maximizing a non-monotone submodular function under the intersection of I and d knapsack constraints  ...  We develop the first efficient single pass streaming algorithm, Streaming Local Search, that for any streaming monotone submodular maximization algorithm with approximation guarantee α under a collection  ...  This research was partially supported by ERC StG 307036, and NSF CAREER 1553284.  ... 
arXiv:1706.03583v3 fatcat:j3d5wz7m6vdkfjvdzeyahgv3u4

Non-monotone submodular maximization under matroid and knapsack constraints

Jon Lee, Vahab S. Mirrokni, Viswanath Nagarajan, Maxim Sviridenko
2009 Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09  
In this paper, we give the first constant-factor approximation algorithm for maximizing any non-negative submodular function subject to multiple matroid or knapsack constraints.  ...  We emphasize that our results are for non-monotone submodular functions. In particular, for any constant k, we present a " * Supported by an IBM graduate fellowship and NSF award CCF-0728841.  ...  Our original proof [35] was more complicated -we thank Jan for letting us present this simplified proof.  ... 
doi:10.1145/1536414.1536459 dblp:conf/stoc/LeeMNS09 fatcat:262larfgkfcdnmyogqcpayxd5a

Fast Constrained Submodular Maximization: Personalized Data Summarization

Baharan Mirzasoleiman, Ashwinkumar Badanidiyuru, Amin Karbasi
2016 International Conference on Machine Learning  
FANTOM maximizes a submodular function (not necessarily monotone) subject to the intersection of a p-system and l knapsacks constrains.  ...  We develop the first practical and FAst coNsTrained submOdular Maximization algorithm, FANTOM, with strong theoretical guarantees.  ...  Table 1 . 1 Comparison of running times and approximation ratios for non-monotone submodular maximization under different constraints.  ... 
dblp:conf/icml/MirzasoleimanBK16 fatcat:vlefgd7cqjaydpbwo3p4ckxrlq

Maximizing non-monotone submodular set functions subject to different constraints: Combined algorithms

Salman Fadaei, MohammadAmin Fazli, MohammadAli Safari
2011 Operations Research Letters  
As an application of this technique we get a 0.13-approximation for maximizing non-monotone submodular functions subject to both matroid and multiple knapsacks.  ...  It appears that that our approach could be combined with pipage rounding or randomized swap rounding and provide approximation algorithms for various constrained maximization problems over non-monotone  ...  Dara Moazzami, and Jasem Fadaei for their help and advice.  ... 
doi:10.1016/j.orl.2011.10.002 fatcat:fksx7yrwfjg43g2bi4nkinze6i

A Unified Continuous Greedy Algorithm for Submodular Maximization

M. Feldman, Joseph Naor, R. Schwartz
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
Some notable immediate implications are an improved 1/e-approximation for maximizing a non-monotone submodular function subject to a matroid or O(1)-knapsack constraints, and information-theoretic tight  ...  approximations for Submodular Max-SAT and Submodular Welfare with k players, for any number of players k.  ...  Consider the problem of maximizing a non-monotone submodular function subject to a constant number of knapsack constraints.  ... 
doi:10.1109/focs.2011.46 dblp:conf/focs/FeldmanNS11 fatcat:ajjddbnuwzcjxd23rcwup2ptne

Filtered Search for Submodular Maximization with Controllable Approximation Bounds

Wenlin Chen, Yixin Chen, Kilian Q. Weinberger
2015 International Conference on Artificial Intelligence and Statistics  
FS naturally handles monotone and nonmonotone functions as well as unconstrained problems and problems with cardinality, matroid, and knapsack constraints.  ...  Most existing submodular maximization algorithms provide theoretical guarantees with approximation bounds.  ...  Chen and Y. Chen were partially supported by the CNS-1017701, CCF-1215302, IIS-1343896, and DBI-1356669 grants from the National Science Foundation of the US. K.Q.  ... 
dblp:conf/aistats/ChenCW15 fatcat:eukwq6pe6zd6tczvz35jann4t4

Non-monotone submodular maximization under matroid and knapsack constraints [article]

Jon Lee, Vahab Mirrokni, Viswanath Nagarjan, Maxim Sviridenko
2009 arXiv   pre-print
For the problem of maximizing a non-monotone submodular function, Feige, Mirrokni, and Vondrák recently developed a 2 5-approximation algorithm FMV07, however, their algorithms do not handle side constraints  ...  In this paper, we give the first constant-factor approximation algorithm for maximizing any non-negative submodular function subject to multiple matroid or knapsack constraints.  ...  Our original proof [35] was more complicated -we thank Jan for letting us present this simplified proof.  ... 
arXiv:0902.0353v1 fatcat:ayzfv2mygjhc5esgfqwv2vbceu

Differentially Private Monotone Submodular Maximization Under Matroid and Knapsack Constraints

Omid Sadeghi, Maryam Fazel
2021 International Conference on Artificial Intelligence and Statistics  
In this paper, we study the general framework of nonnegative monotone submodular maximization subject to matroid or knapsack constraints in both offline and online settings.  ...  Numerous tasks in machine learning and artificial intelligence have been modeled as submodular maximization problems.  ...  monotone submodular maximization subject to matroid or knapsack constraints and we analyze its performance in both settings.  ... 
dblp:conf/aistats/SadeghiF21 fatcat:3qqz7mp2hrgf7hqb5ufvhhdgzq

Beyond Pointwise Submodularity: Non-Monotone Adaptive Submodular Maximization subject to Knapsack and k-System Constraints [article]

Shaojie Tang
2021 arXiv   pre-print
In this paper, we study the non-monotone adaptive submodular maximization problem subject to a knapsack and a k-system constraints.  ...  Inspired by two recent studies on non-monotone adaptive submodular maximization, we develop a sampling-based randomized algorithm that achieves a 1/10 approximation for the case of a knapsack constraint  ...  In this paper, we propose the first constant approximation solutions for maximizing a non-monotone adaptive submodular function under a knapsack and a k-system constraints.  ... 
arXiv:2104.04853v4 fatcat:wnitb6axfrb4zmu6qo2ceomlre

Submodular function maximization via the multilinear relaxation and contention resolution schemes

Jan Vondrák, Chandra Chekuri, Rico Zenklusen
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
knapsack constraints, and their intersections.  ...  Our results provide a broadly applicable framework for maximizing linear and submodular functions subject to independence constraints. We give several illustrative examples.  ...  Acknowledgments: We thank Mohit Singh for helpful discussions on contention resolution schemes for matroids.  ... 
doi:10.1145/1993636.1993740 dblp:conf/stoc/VondrakCZ11 fatcat:mqevhorqgfecjhj73gxbtbw3jy

Constrained Non-monotone Submodular Maximization: Offline and Secretary Algorithms [chapter]

Anupam Gupta, Aaron Roth, Grant Schoenebeck, Kunal Talwar
2010 Lecture Notes in Computer Science  
Our idea of using existing algorithms for monotone functions to solve the non-monotone case also works for maximizing a submodular function with respect to a knapsack constraint: we get a simple greedy-based  ...  Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone.  ...  Vondrák, and especially R.D. Kleinberg for valuable comments, suggestions, and conversations.  ... 
doi:10.1007/978-3-642-17572-5_20 fatcat:gzb4mt7lnrgyndal6pj2lkqwju

Submodular Function Maximization via the Multilinear Relaxation and Contention Resolution Schemes

Chandra Chekuri, Jan Vondrák, Rico Zenklusen
2014 SIAM journal on computing (Print)  
knapsack constraints, and their intersections.  ...  Our results provide a broadly applicable framework for maximizing linear and submodular functions subject to independence constraints. We give several illustrative examples.  ...  Acknowledgments: We thank Mohit Singh for helpful discussions on contention resolution schemes for matroids.  ... 
doi:10.1137/110839655 fatcat:a3cz23jdzfbttjdwfkbyofxypa

Subspace Selection via DR-Submodular Maximization on Lattices

So Nakashima, Takanori Maehara
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We also prove the "quantum version" of the cut function is a non-monotone directional DR submodular function.  ...  selection problem in certain instances.We show that, under several constraints, the directional DRsubmodular function maximization problem can be solved efficiently with provable approximation factors  ...  We propose approximation algorithms for maximizing (1) monotone downward DR-submodular function over height constraint, (2) monotone downward DR-submodular function over knapsack constraint, and (3) non-monotone  ... 
doi:10.1609/aaai.v33i01.33014618 fatcat:2we5whxzenb5nfc5my2ibx6uuu
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