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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.  ...  In the case of a single knapsack, our analysis suggests that the standard greedy can be used in non-monotone settings.  ...  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

Near Optimal Dynamic Mobile Advertisement Offloading with Time Constraints

Wanru Xu, Chaocan Xiang, Chang Tian
2019 IEEE Access  
In dealing with this difficulty, we fortunately find that this problem could be transformed into a maximizing monotone submodular set function, which is subject to partition matroid constraints.  ...  As far as we know, EIMP is a combination of the 0-1 multi-dimensional and multiple knapsack problem, which is even harder.  ...  any non-negative submodular function subject to multiple matroid or knapsack constraints, but it focused on the non-monotone submodular functions.  ... 
doi:10.1109/access.2019.2934825 fatcat:mi2tztmov5eyjauzozkieoprlu

General Knapsack Problems in a Dynamic Setting [article]

Yaron Fairstein, Ariel Kulik, Joseph Naor, Danny Raz
2021 arXiv   pre-print
The multistage model was introduced with this goal in mind.  ...  In this paper we consider the Generalized Multistage d-Knapsack problem, a generalization of the multistage variants of the Multiple Knapsack problem, as well as the d-Dimensional Knapsack problem.  ...  . , T function p t is non-negative, monotone and submodular. Thus, due to Claim 21, functions (p t ) T t=1 are also non-negative, monotone and submodular.  ... 
arXiv:2105.00882v2 fatcat:7mvu7o5am5dobe4pstnokb75ma

Budgeted Influence Maximization for Multiple Products [article]

Nan Du, Yingyu Liang, Maria Florina Balcan, Le Song
2014 arXiv   pre-print
In this paper, we provide a novel solution by formulating the problem as a submodular maximization in a continuous-time diffusion model under an intersection of a matroid and multiple knapsack constraints  ...  The typical algorithmic problem in viral marketing aims to identify a set of influential users in a social network, who, when convinced to adopt a product, shall influence other users in the network and  ...  A.2 Non-uniform cost We first prove that a theorem for Problem 3 with general normalized monotonic submodular function f (S) and general P (Theorem 7), and then specify the guarantee for our influence  ... 
arXiv:1312.2164v2 fatcat:s3yvg7awtnbfnm52zsjo5jznzy

Pareto Optimization for Subset Selection with Dynamic Cost Constraints [article]

Vahid Roostapour, Aneta Neumann, Frank Neumann, Tobias Friedrich
2020 arXiv   pre-print
Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that B increases.  ...  Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.  ...  Acknowledgement We thank Chao Qian for providing his POMC and EAMC implementations and test data to carry out our experimental investigations.  ... 
arXiv:1811.07806v2 fatcat:p2zt3tiz2rewve36ergon4neje

A Survey on Recent Progress in the Theory of Evolutionary Algorithms for Discrete Optimization [article]

Benjamin Doerr, Frank Neumann
2021 arXiv   pre-print
stochastic and dynamic problems.  ...  We regard how evolutionary algorithms optimize submodular functions and we give an overview over the large body of recent results on estimation of distribution algorithms.  ...  Acknowledgements Frank Neumann has been support by the Alexander von Humboldt Foundation through a Humboldt Fellowship for Experienced Researchers and by the Australian Research Council through grant FT200100536  ... 
arXiv:2006.16709v3 fatcat:cm23qxphufdpvntoilo5idsioa

Deletion-Robust Submodular Maximization: Data Summarization with "the Right to be Forgotten"

Baharan Mirzasoleiman, Amin Karbasi, Andreas Krause
2017 International Conference on Machine Learning  
Motivated by this challenge, we introduce the dynamic deletion-robust submodular maximization problem.  ...  We develop the first resilient streaming algorithm, called ROBUST-STREAMING, with a constant factor approximation guarantee to the optimum solution.  ...  This work was done in part while Amin Karbasi, and Andreas Krause were visiting the Simons Institute for the Theory of Computing.  ... 
dblp:conf/icml/MirzasoleimanK017 fatcat:34h5vr4adrhgrmmm5zixf6k2vu

A Framework towards Domain Specific Video Summarization [article]

Vishal Kaushal, Sandeep Subramanian, Suraj Kothawade, Rishabh Iyer and Ganesh Ramakrishnan
2018 arXiv   pre-print
We also argue that ratings can be seen as unified representation of all possible ground truth summaries of a video, taking us one step closer in dealing with challenges associated with multiple ground  ...  It leverages the ratings information and is richer in appropriately modeling desirable and undesirable characteristics of a summary.  ...  For λ > 0.5 it is non-monotone submodular.  ... 
arXiv:1809.08854v2 fatcat:csd2am5oqvhj5eenbhlvmkhv2m

Priority Lists for Power System Investments: Locating Phasor Measurement Units

Ilgiz Murzakhanov, David Pozo
2021 2021 IEEE Madrid PowerTech  
We show that i) our framework is consistent with the evolution of power system upgrades, and ii) in particular circumstances, both frameworks provide the same solution if the problem satisfies submodularity  ...  Decision-making tools often support the selection of the best set of components to upgrade. Optimization models are often used to support decision making at a given point in time.  ...  In the original knapsack problem, a set of items with known weights and values is given. We aim to pick the items with a maximum total value while the total weight must not exceed a set limit.  ... 
doi:10.1109/powertech46648.2021.9494959 fatcat:4shktleoqbeqfkeeb2wwoboqpq

Multi-agent Time-based Decision-making for the Search and Action Problem [article]

Takahiro Miki, Marija Popovic, Abel Gawel, Gregory Hitz, Roland Siegwart
2018 arXiv   pre-print
The main idea is to treat time as an allocated budget in a setting where each agent action incurs a time cost and yields a certain reward.  ...  Many robotic applications, such as search-and-rescue, require multiple agents to search for and perform actions on targets.  ...  To do this, we cast Eq. 1 as the well-known knapsack problem and solve it using dynamic programming [21] .  ... 
arXiv:1802.10147v2 fatcat:oy7jqgnpsbftnjj2bxbpkoojge

Coordinated sampling sans Origin-Destination identifiers: Algorithms and analysis

Vyas Sekar, Anupam Gupta, Michael K. Reiter, Hui Zhang
2010 2010 Second International Conference on COMmunication Systems and NETworks (COMSNETS 2010)  
Leveraging results from the theory of maximizing submodular set functions, cSamp-T provides near-ideal performance in maximizing the total flow coverage in the network.  ...  Further, with a small amount of targeted upgrades to a few routers, cSamp-T nearly optimally maximizes the minimum fractional coverage across all OD-pairs.  ...  This work was supported in part by NSF awards CNS-0756998 and ANI-0331653.  ... 
doi:10.1109/comsnets.2010.5432011 dblp:conf/comsnets/SekarGRZ10 fatcat:jodtukxjejeo5d5z76x6r7ch24

Mobility-Aware Traffic Offloading via Cooperative Coded Edge Caching

Dewang Ren, Xiaolin Gui, Kaiyuan Zhang, Jie Wu
2020 IEEE Access  
Each subproblem is converted into a submodular optimization problem, and a request-aware distributed replacement algorithm with linear computational complexity is proposed.  ...  Accordingly, in this paper, we propose a mobility-aware and cooperative coded caching (MoCoCoCa) for achieving traffic offloading in MENs, by considering user mobility and hard service deadline constraints  ...  It is proven to satisfy Proposition 1, and thus, V (X ) is a monotone submodular set function.  ... 
doi:10.1109/access.2020.2977990 fatcat:5eiykiutfranfpwiz5bcp5taoi

Priority Lists for Power System Investments: Locating Phasor Measurement Units [article]

Ilgiz Murzakhanov, David Pozo
2021 arXiv   pre-print
We show that i) our framework is consistent with the evolution of power system upgrades, and ii) in particular circumstances, both frameworks provide the same solution if the problem satisfies submodularity  ...  Decision-making tools often support the selection of the best set of components to upgrade. Optimization models are often used to support decision making at a given point in time.  ...  In the original knapsack problem, a set of items with known weights and values is given. We aim to pick the items with a maximum total value while the total weight must not exceed a set limit.  ... 
arXiv:2104.05071v1 fatcat:box4zwyh45ablnntc5kcqepjem

Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs [article]

Paul Dütting, Michal Feldman, Thomas Kesselheim, Brendan Lucier
2017 arXiv   pre-print
We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints.  ...  to stochastic settings.  ...  Auction MPH-k Static, anonymous item prices O(k 2 ) [23] 4k − 2 [this work] MPH, Demand Matroid Submodular Dynamic prices 2 (existential) 4 (computational) Value Knapsack Additive Static  ... 
arXiv:1612.03161v2 fatcat:exaa5jinkbdshbq2bl7dvzb3vq

Analysis of influence maximization in temporal social networks

Qiu Liqing, Yu Jinfeng, Fan Xin, Jia Wei, Gao Wenwen
2019 IEEE Access  
However, the most existing work is limited to the static social network and ignores the role of time in information propagation.  ...  In this paper, we analyze the influence maximization problem in temporal social networks and present a greedy-based on the latency-aware independent cascade (GLAIC) algorithm enhanced by cost-effective  ...  [14] formulated the user, monetary, and timing constraints problem as a submodular maximization task in a continuous-time diffusion model under the intersection of one matroid and multiple knapsack  ... 
doi:10.1109/access.2019.2894155 fatcat:3zt6whdoeja3rkjqbm3prdo26e
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