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Fairness in Streaming Submodular Maximization: Algorithms and Hardness [article]

Marwa El Halabi, Slobodan Mitrović, Ashkan Norouzi-Fard, Jakab Tardos, Jakub Tarnawski
2020 arXiv   pre-print
To this end, we develop the first streaming approximation algorithms for submodular maximization under fairness constraints, for both monotone and non-monotone functions.  ...  Submodular maximization has become established as the method of choice for the task of selecting representative and diverse summaries of data.  ...  Acknowledgments and Disclosure of Funding  ... 
arXiv:2010.07431v2 fatcat:tzmdn4rnljcepa3nuew7m476tq

Streaming Submodular Maximization with Fairness Constraints [article]

Yanhao Wang and Francesco Fabbri and Michael Mathioudakis
2020 arXiv   pre-print
We propose efficient algorithms for this fairness-aware variant of the streaming submodular maximization problem.  ...  In addition, we design a single-pass streaming algorithm that has the same (1/2-ε) approximation ratio when unlimited buffer size and post-processing time is permitted.  ...  Yanhao Wang and Michael Mathioudakis have been supported by the MLDB project of Academy of Finland (decision number: 322046).  ... 
arXiv:2010.04412v1 fatcat:hzd5qcuwt5exzexb5lhxfnr27m

Streaming submodular maximization

Ashwinkumar Badanidiyuru, Baharan Mirzasoleiman, Amin Karbasi, Andreas Krause
2014 Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '14  
We develop the first efficient streaming algorithm with constant factor 1/2 − ε approximation guarantee to the optimum solution, requiring only a single pass through the data, and memory independent of  ...  Thus, such problems can be reduced to maximizing a submodular set function subject to a cardinality constraint. Classical approaches to submodular maximization require full access to the data set.  ...  Towards Streaming Submodular Maximization. The standard greedy algorithm (4) requires access to all elements of the ground set and hence cannot be directly applied in the streaming setting.  ... 
doi:10.1145/2623330.2623637 dblp:conf/kdd/BadanidiyuruMKK14 fatcat:ybb6hl24fzg7hjh742tyswd2nm

Differentially Private Online Submodular Maximization [article]

Sebastian Perez-Salazar, Rachel Cummings
2020 arXiv   pre-print
In this work we consider the problem of online submodular maximization under a cardinality constraint with differential privacy (DP).  ...  A stream of T submodular functions over a common finite ground set U arrives online, and at each time-step the decision maker must choose at most k elements of U before observing the function.  ...  While (unconstrained) submodular minimization can be solved with polynomial number of oracle calls (Schrijver, 2003; Bach, 2013) , submodular maximization is known to be NP-hard for general submodular  ... 
arXiv:2010.12816v1 fatcat:jbciay4wxregjf6csjkpg7ouiu

The Power of Subsampling in Submodular Maximization [article]

Christopher Harshaw, Ehsan Kazemi, Moran Feldman, Amin Karbasi
2021 arXiv   pre-print
We propose subsampling as a unified algorithmic technique for submodular maximization in centralized and online settings.  ...  In the streaming setting, we present SampleStreaming, which obtains a (4p +2 - o(1))-approximation for maximizing a submodular function subject to a p-matchoid using O(k) memory and O(km/p) evaluation  ...  This work was supported in part by NSF (IIS-1845032), ONR (N00014-19-1-2406), and AFOSR (FA9550-18-1-0160) awarded to Amin Karbasi and an NSF Graduate Research Fellowship (DGE1122492) awarded to Christopher  ... 
arXiv:2104.02772v1 fatcat:jh2fgeuwuvgsdbh4gzbztemkb4

Fast Budgeted Influence Maximization over Multi-Action Event Logs [article]

Qilian Yu, Hang Li, Yun Liao, Shuguang Cui
2018 arXiv   pre-print
Based on this model, influence maximization is formulated as a submodular maximization problem under a general knapsack constraint, which is NP-hard.  ...  ., a cardinality constraint, and show that the developed streaming algorithm can achieve (1/2-ϵ)-approximation of the optimality.  ...  Therefore, problem (7) is a submodular maximization problem under a knapsack constraint, which has been proved to be NP-hard [19] .  ... 
arXiv:1710.02141v3 fatcat:fkprt55iijbprhkjddualwswuy

Submodular Maximization in Clean Linear Time [article]

Wenxin Li, Moran Feldman, Ehsan Kazemi, Amin Karbasi
2022 arXiv   pre-print
In this paper, we provide the first deterministic algorithm that achieves the tight 1-1/e approximation guarantee for submodular maximization under a cardinality (size) constraint while making a number  ...  Finally, we extend our results to the general case of maximizing a monotone submodular function subject to the intersection of a p-set system and multiple knapsack constraints.  ...  Among the first semi-streaming algorithms for submodular maximization was the work of Badanidiyuru et al.  ... 
arXiv:2006.09327v5 fatcat:v3gv3h5xmvf3pmh466cgq4shv4

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

Anupam Gupta, Aaron Roth, Grant Schoenebeck, Kunal Talwar
2010 Lecture Notes in Computer Science  
[LMNS09, LSV09] gave the first algorithms for these problems via local-search algorithms: in this paper, we consider greedy approaches that have been successful for monotone submodular maximization, and  ...  Our greedy-based algorithm has a run-time polynomial in , and hence give polynomial-time algorithms for even non-constant values of . • We give a constant-factor approximation for maximizing submodular  ...  Vondrák, and especially R.D. Kleinberg for valuable comments, suggestions, and conversations.  ... 
doi:10.1007/978-3-642-17572-5_20 fatcat:gzb4mt7lnrgyndal6pj2lkqwju

Influence Maximization on Social Graphs: A Survey

Yuchen Li, Ju Fan, Yanhao Wang, Kian-Lee Tan
2018 IEEE Transactions on Knowledge and Data Engineering  
Influence Maximization (IM), which selects a set of k users (called seed set) from a social network to maximize the expected number of influenced users (called influence spread), is a key algorithmic problem  ...  In this paper, we survey and synthesize a wide spectrum of existing studies on IM from an algorithmic perspective, with a special focus on the following key aspects: (1) a review of well-accepted diffusion  ...  They define the influence between users in the sliding window model and propose the Stream Influence Maximization (SIM) query to continuously track a seed set maximizing the influence wrt. the current  ... 
doi:10.1109/tkde.2018.2807843 fatcat:f6vnhknlevckbkqwkkqotgalc4

Online Multistage Subset Maximization Problems [article]

Evripidis Bampis, Bruno Escoffier, Kevin Schewior, Alexandre Teiller
2019 arXiv   pre-print
We study multistage subset maximization problems in the online setting, that is, p_t (along with possibly F_t) only arrive one by one and, upon such an arrival, the online algorithm has to output the corresponding  ...  online algorithm.  ...  They also showed that the maximization version of the problem admits a constant factor approximation algorithm, but is APX-hard.  ... 
arXiv:1905.04162v1 fatcat:ajf73mqu7bcmbalxpk7fjqcwpm

The One-way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness [article]

Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, Rico Zenklusen
2020 arXiv   pre-print
This improves on a prior 1-1/e+ε hardness and matches, up to an arbitrarily small margin, the best known approximation algorithm.  ...  Moreover, exploiting the link of our model to streaming, we settle the approximability for streaming algorithms by presenting a tight 1/2+ε hardness result, based on the construction of a new family of  ...  This is also the case for submodular functions. As we show below, our results yield both new hardness and algorithmic results in the context of data streams and robustness. Data stream algorithms.  ... 
arXiv:2003.13459v1 fatcat:dea4oconzraajf764fwnvolrl4

Maximizing Social Welfare in a Competitive Diffusion Model [article]

Prithu Banerjee, Wei Chen, Laks V.S. Lakshmanan
2020 arXiv   pre-print
The problem in general is not only NP-hard but also NP-hard to approximate within any constant factor.  ...  Influence maximization (IM) has garnered a lot of attention in the literature owing to applications such as viral marketing and infection containment.  ...  While fairness in IM has been studied recently, incorporating fairness in social welfare maximization will be an interesting challenge.  ... 
arXiv:2012.03354v1 fatcat:dgefya5opfez5fn2is27dp3b5m

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
Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing.  ...  We present a simple randomized greedy algorithm that achieves a 5.83 approximation and runs in O(n log n) time, i.e., at least a factor n faster than other state-of-the-art algorithms.  ...  There is extensive research focusing on this issue, be it in the standard algorithmic setting [39] , or in streaming [9, 3] and distributed submodular maximization [38, 12] .  ... 
arXiv:2007.05014v1 fatcat:ynt4meyn7jfulen6c6idgc4yc4

Deterministic Approximation for Submodular Maximization over a Matroid in Nearly Linear Time [article]

Kai Han, Zongmai Cao, Shuang Cui, Benwei Wu
2020 arXiv   pre-print
We study the problem of maximizing a non-monotone, non-negative submodular function subject to a matroid constraint.  ...  We show that this deterministic ratio can be improved to 1/4 under 𝒪(nr) time complexity, and then present a more practical algorithm dubbed TwinGreedyFast which achieves 1/4-ϵ deterministic ratio in  ...  As it needs to call an unconstrained submodular maximization (USM) algorithm, we use the USM algorithm proposed in [12] with 1/3 deterministic ratio and linear running time.  ... 
arXiv:2010.11420v1 fatcat:likipanpybcfra56r5zcgp6dfy

Influence Maximization with Bandits [article]

Sharan Vaswani, Laks.V.S. Lakshmanan, Mark Schmidt
2016 arXiv   pre-print
We consider the problem of influence maximization, the problem of maximizing the number of people that become aware of a product by finding the 'best' set of 'seed' users to expose the product to.  ...  Beyond our theoretical results, we describe a practical implementation and experimentally demonstrate its efficiency and effectiveness on four real datasets.  ...  IM is NP-hard under standard diffusion models, the expected spread function σ D (S) is monotone and submodular.  ... 
arXiv:1503.00024v4 fatcat:t4mpggny2zgtdbrm4wc35iljrq
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