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Online submodular welfare maximization: Greedy is optimal [article]

Michael Kapralov, Ian Post, Jan Vondrak
2013 arXiv   pre-print
Since the Greedy algorithm is known to be 1/2-competitive for monotone submodular valuations, of which coverage is a special case, this proves that Greedy provides the optimal competitive ratio.  ...  We prove that no online algorithm (even randomized, against an oblivious adversary) is better than 1/2-competitive for welfare maximization with coverage valuations, unless NP = RP.  ...  Online welfare maximization.  ... 
arXiv:1204.1025v2 fatcat:4ya752d3zbfmzg5cdemi2d5d3a

Online submodular welfare maximization: Greedy is optimal [chapter]

Michael Kapralov, Ian Post, Jan Vondrák
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
Since the Greedy algorithm is known to be 1/2-competitive for monotone submodular valuations, of which coverage is a special case, this proves that Greedy provides the optimal competitive ratio.  ...  We prove that no online algorithm (even randomized, against an oblivious adversary) is better than 1/2-competitive for welfare maximization with coverage valuations, unless N P = RP .  ...  Online welfare maximization.  ... 
doi:10.1137/1.9781611973105.88 dblp:conf/soda/KapralovPV13 fatcat:3y53ez722fbhjdgwgpaqigg7pm

Online Submodular Welfare Maximization

Nitish Korula, Vahab Mirrokni, Morteza Zadimoghaddam
2015 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15  
In the Submodular Welfare Maximization (SWM) problem, the input consists of a set of n items, each of which must be allocated to one of m agents.  ...  Sm in order to maximize the social welfare, defined as m =1 v (S ).  ...  The Submodular Welfare Maximization problem has been studied extensively as both an offline and an online optimization problem: For the offline optimization problem, one can easily observe that SWM is  ... 
doi:10.1145/2746539.2746626 dblp:conf/stoc/KorulaMZ15 fatcat:s2ea4ksdr5aprenrtnk4562fai

Online Submodular Welfare Maximization: Greedy Beats 1/2 in Random Order [article]

Nitish Korula, Vahab Mirrokni, Morteza Zadimoghaddam
2017 arXiv   pre-print
We solve this open problem by demonstrating that the greedy algorithm has a competitive ratio of at least 0.505 for the Online Submodular Welfare Maximization problem in the random order model.  ...  S_m in order to maximize the social welfare, defined as ∑_ℓ = 1^m v_ℓ(S_ℓ). In this paper, we consider the online version of SWM.  ...  The Submodular Welfare Maximization problem has been studied extensively as both an offline and an online optimization problem: For the offline optimization problem, one can easily observe that SWM is  ... 
arXiv:1712.05450v1 fatcat:qhovusdvr5flfas4wu7nmlvhzm

Whole-Page Optimization and Submodular Welfare Maximization with Online Bidders

Nikhil R. Devanur, Zhiyi Huang, Nitish Korula, Vahab S. Mirrokni, Qiqi Yan
2016 ACM Transactions on Economics and Computation  
Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem.  ...  In this paper, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation  ...  Relationship to Online Submodular Welfare Maximization.  ... 
doi:10.1145/2892563 fatcat:6nz4kknsgbarfdvgep33knh6li

Whole-page optimization and submodular welfare maximization with online bidders

Nikhil R. Devanur, Zhiyi Huang, Nitish Korula, Vahab S. Mirrokni, Qiqi Yan
2013 Proceedings of the fourteenth ACM conference on Electronic commerce - EC '13  
Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem.  ...  In this paper, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation  ...  Relationship to Online Submodular Welfare Maximization.  ... 
doi:10.1145/2492002.2482603 dblp:conf/sigecom/Devanur0KMY13 fatcat:en7toehxlvgx3ahj2g7ilgys5m

Submodular Welfare Maximization [article]

Samira Samadi
2013 arXiv   pre-print
An overview of different variants of the submodular welfare maximization problem in combinatorial auctions.  ...  In particular, I studied the existing algorithmic and game theoretic results for submodular welfare maximization problem and its applications in other areas such as social networks.  ...  Results on offline and online welfare maximization are given in the following.  ... 
arXiv:1311.5603v1 fatcat:6jc4abmdxbdgdb2vkx4cfabjsy

Submodular Maximization using Test Scores [article]

Shreyas Sekar, Milan Vojnovic, Se-Young Yun
2019 arXiv   pre-print
We then extend our results to the more general stochastic submodular welfare maximization problem, where the goal is to select items and assign them to multiple groups to maximize the sum of the expected  ...  We study the canonical problem of maximizing a stochastic submodular function subject to a cardinality constraint, where the goal is to select a subset from a ground set of items with uncertain individual  ...  The proof is similar in spirit to that of the 1 2 -approximate greedy algorithm for submodular welfare maximization proposed by Lehmann et al. (2006) .  ... 
arXiv:1605.07172v4 fatcat:ttpccnarizbdjcfacdy3qldi44

Approximating special social influence maximization problems

Jie Wu, Ning Wang
2020 Tsinghua Science and Technology  
Social Influence Maximization Problems (SIMPs) deal with selecting k seeds in a given Online Social Network (OSN) to maximize the number of eventually-influenced users.  ...  One is a profit-maximization SIMP where seed selection cost is included in the overall utility function, breaking the monotone property.  ...  Monotone but non-submodular: The welfare maximization problem is as follows: there is a set of players and a set of indivisible items.  ... 
doi:10.26599/tst.2019.9010017 fatcat:fjenih5sozdupcc24lgxsi4izm

Maximizing Sequence-Submodular Functions and its Application to Online Advertising [article]

Saeed Alaei, Ali Makhdoumi, Azarakhsh Malekian
2019 arXiv   pre-print
We establish that if the objective function is sequence-submodular and sequence-non-decreasing, then there exists a greedy algorithm that achieves 1-1/e of the optimal solution.  ...  Motivated by applications in online advertising, we consider a class of maximization problems where the objective is a function of the sequence of actions as well as the running duration of each action  ...  The greedy approach is a natural tool to solve maximization problems with a submodular objective function.  ... 
arXiv:1009.4153v4 fatcat:jhd52royobf7vc6dc5wi67qn7q

Scalable and distributed submodular maximization with matroid constraints

Andrew Clark, Basel Alomair, Linda Bushnell, Radha Poovendran
2015 2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)  
Our key step is to construct an auxiliary function from the submodular objective function, and develop distributed exchange-based algorithms for optimizing the auxiliary function.  ...  We prove that both algorithms provide (1-1/e) optimality bounds, and hence achieve the same guarantees as the best centralized algorithms. A. Clark is with the  ...  In [5] , a distributed greedy algorithm was proposed for cardinality-constrained submodular maximization.  ... 
doi:10.1109/wiopt.2015.7151103 dblp:conf/wiopt/ClarkABP15 fatcat:of4s2m4oknfi5aumuq2ahs4cem

Online Submodular Maximization: Beating 1/2 Made Simple [article]

Niv Buchbinder, Moran Feldman, Yuval Filmus, Mohit Garg
2018 arXiv   pre-print
The Submodular Welfare Maximization problem (SWM) captures an important subclass of combinatorial auctions and has been studied extensively from both computational and economic perspectives.  ...  In this setting, it is well known that the greedy algorithm achieves a competitive ratio of 1/2, and recently Kapralov et al. (2013) showed that this ratio is optimal for the problem.  ...  It is well known that for this online setting the greedy approach that allocates each item to the bidder with the currently maximal marginal gain for the item is 1 /2-competitive, which is the optimal  ... 
arXiv:1807.05529v2 fatcat:3ybwojhvtnf7begkyohj75n6fi

Maximizing Stochastic Monotone Submodular Functions [article]

Arash Asadpour, Hamid Nazerzadeh
2015 arXiv   pre-print
We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint.  ...  We show that the adaptivity gap -- the ratio between the values of optimal adaptive and optimal non-adaptive policies -- is bounded and is equal to e/(e-1).  ...  We acknowledge that the example is section 3.1 was brought to our attention by Jan Vondrák.  ... 
arXiv:0908.2788v3 fatcat:uyy7jcwjnncwlh6iy4uoyrvklu

Traffic Shaping in E-Commercial Search Engine: Multi-Objective Online Welfare Maximization

Liucheng Sun, Chenwei Weng, Chengfu Huo, Weijun Ren, Guochuan Zhang, Xin Li
2021 AAAI Conference on Artificial Intelligence  
This paper presents a unified framework from the aspect of multi-objective welfare maximization where we regard all business requirements as objectives to optimize.  ...  The e-commercial search engine is the primary gateway for customers to find desired products and engage in online shopping.  ...  Acknowledgments This work is supported by Science and Technology Innovation 2030 -"New Generation Artificial Intelligence" Major Project (No. 2018AAA0100902), China.  ... 
dblp:conf/aaai/SunWHRZL21 fatcat:yzgrjeva6vevrosmw3pbifflvm

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

Anupam Gupta, Aaron Roth, Grant Schoenebeck, Kunal Talwar
2010 arXiv   pre-print
Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone.  ...  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  ...  Optimal approximation for the submodular welfare problem in the value oracle model.  ... 
arXiv:1003.1517v2 fatcat:aavnftsxtjfrpo7weqnmna37cu
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