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Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint [article]

Georgios Amanatidis, Federico Fusco, Philip Lazos, Stefano Leonardi, Rebecca Reiffenhäuser
2020 arXiv   pre-print
Focusing on these challenges, we revisit the classic problem of maximizing a (possibly non-monotone) submodular function subject to a knapsack constraint.  ...  There, we obtain a 9-approximation to the best adaptive policy, which is the first constant approximation for non-monotone objectives.  ...  We focus on two applications that fit within the framework of non-monotone submodular maximization subject to a knapsack constraint, namely video recommendation and influence-and-exploit marketing.  ... 
arXiv:2007.05014v1 fatcat:ynt4meyn7jfulen6c6idgc4yc4

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

Anupam Gupta, Aaron Roth, Grant Schoenebeck, Kunal Talwar
2010 Lecture Notes in Computer Science  
functions subject to a knapsack constraint.  ...  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  ...  [KST09] recently showed that one could get essentially the same approximation subject to a constant number of knapsack constraints. Non-Monotone Submodular Maximization.  ... 
doi:10.1007/978-3-642-17572-5_20 fatcat:gzb4mt7lnrgyndal6pj2lkqwju

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  ...  With these simpler algorithms, we are able to adapt our approach to constrained non-monotone submodular maximization to the (online) secretary setting, where elements arrive one at a time in random order  ...  Thanks to C. Chekuri also for pointing out an error in Section B, and to M.T. Hajiaghayi for informing us of the results in [BHZ10] .  ... 
arXiv:1003.1517v2 fatcat:aavnftsxtjfrpo7weqnmna37cu

Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity [article]

Georgios Amanatidis, Federico Fusco, Philip Lazos, Stefano Leonardi, Alberto Marchetti Spaccamela, Rebecca Reiffenhäuser
2021 arXiv   pre-print
In this work we obtain the first constant factor approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with near-optimal O(log n) adaptive complexity.  ...  for the special cases of cardinality constraints or monotone objectives.  ...  We study non-negative, possibly non-monotone, submodular maximization under a knapsack constraint.  ... 
arXiv:2102.08327v1 fatcat:2f7gyomxtjheplis6zwoo56wnm

Nearly Linear Time Deterministic Algorithms for Submodular Maximization Under Knapsack Constraint and Beyond [article]

Wenxin Li
2020 arXiv   pre-print
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond.  ...  +1)-ε) for non-monotone objective.  ...  There is an (1/(p + 7 4 d+ 1)− ε)-approximate algorithm for maximizing a non-negative monotone submodular function subject to a p-system and d knapsack constraints, which performs nearly linear number  ... 
arXiv:1804.08178v6 fatcat:47tudonhwzghpahwwx3h4lzraq

Linear-Time Algorithms for Adaptive Submodular Maximization [article]

Shaojie Tang
2020 arXiv   pre-print
Then we introduce the concept of fully adaptive submodularity, and develop a linear-time algorithm for maximizing a fully adaptive submoudular function subject to a partition matroid constraint.  ...  We start with the well-studied adaptive submodular maximization problem subject to a cardinality constraint. We develop the first linear-time algorithm which achieves a (1-1/e-ϵ) approximation ratio.  ...  ratio when maximizing a monotone submodular function subject to a cardinality constraint.  ... 
arXiv:2007.04214v1 fatcat:gnp46upgnzgvzeftebqaxmp5b4

Budget-Feasible Mechanism Design for Non-Monotone Submodular Objectives: Offline and Online [article]

Georgios Amanatidis, Pieter Kleer, Guido Schäfer
2019 arXiv   pre-print
At the heart of our approach lies a novel greedy algorithm for non-monotone submodular maximization under a knapsack constraint.  ...  The framework of budget-feasible mechanism design studies procurement auctions where the auctioneer (buyer) aims to maximize his valuation function subject to a hard budget constraint.  ...  in line 2 can be any approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint.  ... 
arXiv:1905.00848v2 fatcat:uixdxcmmj5cfhmzom36e6lggt4

Submodular Bandit Problem Under Multiple Constraints [article]

Sho Takemori, Masahiro Sato, Takashi Sonoda, Janmajay Singh, Tomoko Ohkuma
2021 arXiv   pre-print
If there is no uncertainty, this problem is equivalent to a submodular maximization problem under a cardinality constraint.  ...  To solve this problem, we propose a non-greedy algorithm that adaptively focuses on a standard or modified upper-confidence bound.  ...  fast". 3 See footnote in page 2. negative, monotone submodular function with l knapsack constraints and a k-system constraint that achieves 1 (1+ε)(k+2l+1) -approximation solution.  ... 
arXiv:2006.00661v5 fatcat:53wrm635gngwzoracwjrhqmlou

Submodular Function Maximization in Parallel via the Multilinear Relaxation [article]

Chandra Chekuri, Kent Quanrud
2018 arXiv   pre-print
Formally our problem is to maximize F(x) over x ∈ [0,1]^n subject to Ax < 1 where F is the multilinear relaxation of a monotone submodular function.  ...  subject to packing constraints.  ...  In Appendix B, we describe and analyze O log n/ǫ 2 -adaptive algorithms for maximizing a monotone submodular function subject to a single knapsack constraint.  ... 
arXiv:1807.08678v2 fatcat:fe6bim4xvvf37dudlzwekrhypq

Fast Greedy Algorithms in MapReduce and Streaming

Ravi Kumar, Benjamin Moseley, Sergei Vassilvitskii, Andrea Vattani
2015 ACM Transactions on Parallel Computing  
We begin with algorithms for modular maximization subject to a matroid constraint, and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or p-system  ...  We then show how to use this primitive to adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to p-system constraints  ...  We thank Chandra Chekuri for helpful discussions and pointers to relevant work. We thank Sariel Har-Peled for advice on the presentation of this paper.  ... 
doi:10.1145/2809814 fatcat:7kfvywrchzgtbh4oxtyjfz5wg4

Fast greedy algorithms in mapreduce and streaming

Ravi Kumar, Benjamin Moseley, Sergei Vassilvitskii, Andrea Vattani
2013 Proceedings of the 25th ACM symposium on Parallelism in algorithms and architectures - SPAA '13  
We begin with algorithms for modular maximization subject to a matroid constraint, and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or p-system  ...  We then show how to use this primitive to adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to p-system constraints  ...  We thank Chandra Chekuri for helpful discussions and pointers to relevant work. We thank Sariel Har-Peled for advice on the presentation of this paper.  ... 
doi:10.1145/2486159.2486168 dblp:conf/spaa/KumarMVV13 fatcat:2juguc7jtbgpxaupuhilau6sse

Fast algorithms for maximizing submodular functions [chapter]

Ashwinkumar Badanidiyuru, Jan Vondrák
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
In this paper we develop algorithms that match the best known approximation guarantees, but with significantly improved running times, for maximizing a monotone submodular function f : 2 [n] → R + subject  ...  to various constraints.  ...  subject to a cardinality constraint, and a (k + 1)-approximation for maximization of a monotone submodular function subject to k matroid constraints.  ... 
doi:10.1137/1.9781611973402.110 dblp:conf/soda/BadanidiyuruV14 fatcat:xwi5vdpbbzfcldajxndnx5hbha

Beyond Pointwise Submodularity: Non-Monotone Adaptive Submodular Maximization in Linear Time [article]

Shaojie Tang
2020 arXiv   pre-print
In this paper, we study the non-monotone adaptive submodular maximization problem subject to a cardinality constraint.  ...  Our second contribution is to develop the first linear-time algorithm for the non-monotone adaptive submodular maximization problem.  ...  Very recently, (Amanatidis et al. 2020 ) develop a constant approximate solution for maximizing a non-monotone adaptive submodular and pointwise submodular function subject to a knapsack constraint.  ... 
arXiv:2008.05004v3 fatcat:qdektvlaonhmfe7iyrr43m3sym

Non-monotone DR-Submodular Function Maximization [article]

Tasuku Soma, Yuichi Yoshida
2016 arXiv   pre-print
Maximizing non-monotone DR-submodular functions has many applications in machine learning that cannot be captured by submodular set functions.  ...  We consider non-monotone DR-submodular function maximization, where DR-submodularity (diminishing return submodularity) is an extension of submodularity for functions over the integer lattice based on  ...  (Gotovos, Karbasi, and Krause 2015) considered maximizing non-monotone submodular functions in the adaptive setting, a concept introduced in (Golovin and Krause 2011).  ... 
arXiv:1612.00960v1 fatcat:5pxxlfywkjffji6kpg7hxgjrte

A Tight Deterministic Algorithm for the Submodular Multiple Knapsack Problem [article]

Xiaoming Sun, Jialin Zhang, Zhijie Zhang
2021 arXiv   pre-print
Plenty of well-performing approximation algorithms have been designed for the maximization of (monotone or non-monotone) submodular functions over a variety of constraints.  ...  Roughly speaking, the problem asks to maximize a monotone submodular function over multiple bins (knapsacks). Recently, Fairstein et al.  ...  The most relevant problem to SMKP in the field of submodular maximization is maximizing a monotone submodular function subject to multiple linear constraints (SMLC) [21] .  ... 
arXiv:2003.11450v4 fatcat:i55r5ozy2zfurlln5hotamsltm
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