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Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint
[article]
2020
arXiv
pre-print
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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]
2010
Lecture Notes in Computer Science
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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]
2010
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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]
2021
arXiv
pre-print
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2020 pre-print arXiv:2006.00661v3 fatcat:k5kc4y3ifjd5ndbfq7qjr45ffeOther Versions
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]
2018
arXiv
pre-print
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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
2015
ACM Transactions on Parallel Computing
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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
2013
Proceedings of the 25th ACM symposium on Parallelism in algorithms and architectures - SPAA '13
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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]
2013
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
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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]
2020
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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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