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Approximations for Monotone and Nonmonotone Submodular Maximization with Knapsack Constraints

Ariel Kulik, Hadas Shachnai, Tami Tamir
2013 Mathematics of Operations Research  
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 − ε, for any ε > 0, and to obtain a nearly optimal (1−e −1 −ε)−approximation ratio for the monotone case, for any  ...  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  ... 
doi:10.1287/moor.2013.0592 fatcat:calt4f635zaehn37pduhxsl4ce

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

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

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

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  ...  Armed with simpler greedy algorithms for nonmonotone submodular maximization, we are able to perform constrained nonmonotone submodular maximization in several special cases in the secretary setting as  ...  Vondrák, and especially R.D. Kleinberg for valuable comments, suggestions, and conversations.  ... 
doi:10.1007/978-3-642-17572-5_20 fatcat:gzb4mt7lnrgyndal6pj2lkqwju

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.  ...  Some notable applications are an improved 1/e-approximation for maximizing a nonmonotone submodular function subject to a matroid or O(1)-knapsack constraints, and tight approximations for Submodular Max-SAT  ... 
doi:10.1109/focs.2011.46 dblp:conf/focs/FeldmanNS11 fatcat:ajjddbnuwzcjxd23rcwup2ptne

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

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

Constrained Non-Monotone Submodular Maximization: Offline and Secretary Algorithms [article]

Anupam Gupta, Aaron Roth, Grant Schoenebeck, Kunal Talwar
2010 arXiv   pre-print
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. Thanks to C. Chekuri also for pointing out an error in Section B, and to M.T.  ... 
arXiv:1003.1517v2 fatcat:aavnftsxtjfrpo7weqnmna37cu

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

Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints

Jon Lee, Vahab S. Mirrokni, Viswanath Nagarajan, Maxim Sviridenko
2010 SIAM Journal on Discrete Mathematics  
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  ...  Our original proof [35] was more complicated -we thank Jan for letting us present this simplified proof.  ... 
doi:10.1137/090750020 fatcat:fkozckgiyzgtriks4vti5uvbmu

Budget-Feasible Mechanism Design for Non-monotone Submodular Objectives: Offline and Online

Georgios Amanatidis, Pieter Kleer, Guido Schäfer
2022 Mathematics of Operations Research  
At the heart of our approach lies a novel greedy algorithm for non-monotone submodular maximization under a knapsack constraint.  ...  We obtain O(p)-approximation mechanisms for both monotone and non-monotone submodular objectives, when the feasible solutions are independent sets of a p-system.  ...  algorithm for maximizing non-monotone submodular functions subject to a knapsack constraint.  ... 
doi:10.1287/moor.2021.1208 fatcat:jdnz6nti6bf6bmogj6tesiorji

Non-Monotone Submodular Maximization with Multiple Knapsacks in Static and Dynamic Settings [article]

Vanja Doskoč and Tobias Friedrich and Andreas Göbel and Frank Neumann and Aneta Neumann and Francesco Quinzan
2020 arXiv   pre-print
We study the problem of maximizing a non-monotone submodular function under multiple knapsack constraints.  ...  We propose a simple discrete greedy algorithm to approach this problem, and prove that it yields strong approximation guarantees for functions with bounded curvature.  ...  Acknowledgement This work has been supported by the Australian Research Council through grant DP160102401 and by the South Australian Government through the Research Consortium "Unlocking Complex Resources  ... 
arXiv:1911.06791v3 fatcat:32252d5xqvgkffwi3ggdf3iv4y

Multilinear extension of k-submodular functions [article]

Baoxiang Wang, Huanjian Zhou
2021 arXiv   pre-print
For monotone functions, almost 1/2-approximation are obtained under total size and knapsack constraints.  ...  In this paper, we provide a new framework for k-submodular maximization problems, by relaxing the optimization to the continuous space with the multilinear extension of k-submodular functions and rounding  ...  For a monotone k-submodular function with a knapsack constraint, we design the following algorithm to maximize it.  ... 
arXiv:2107.07103v2 fatcat:ursfnj7ctben3d7edkdy2ha4zi

"Bring Your Own Greedy"+Max: Near-Optimal 1/2-Approximations for Submodular Knapsack [article]

Dmitrii Avdiukhin, Grigory Yaroslavtsev, Samson Zhou
2019 arXiv   pre-print
this problem as a submodular maximization subject to a linear (knapsack) constraint.  ...  Instance-specific approximations are typically in the 0.6-0.7 range and frequently beat even the (1-1/e) ≈ 0.63 worst-case barrier for polynomial-time algorithms.  ...  The problem of maximizing a monotone submodular function under a knapsack constraint was introduced by [Wol82] , who gave an algorithm with ≈ 0.35-approximation.  ... 
arXiv:1910.05646v1 fatcat:v3df3bdp3bblnbrold5nzx33xy
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