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Robust Submodular Maximization: A Non-Uniform Partitioning Approach [article]

Ilija Bogunovic, Slobodan Mitrović, Jonathan Scarlett, Volkan Cevher
2017 arXiv   pre-print
In this paper, we solve a key open problem raised therein, presenting a new Partitioned Robust (PRo) submodular maximization algorithm that achieves the same guarantee for more general τ = o(k).  ...  We study the problem of maximizing a monotone submodular function subject to a cardinality constraint k, with the added twist that a number of items τ from the returned set may be removed.  ...  The objective functions in these applications are non-negative, monotone and submodular, and are used in our numerical experiments in Section 5. Robust influence maximization.  ... 
arXiv:1706.04918v1 fatcat:4v3y64jp7vfevitl5jvaaxlwmu

Structured Robust Submodular Maximization: Offline and Online Algorithms [article]

Alfredo Torrico, Mohit Singh, Sebastian Pokutta, Nika Haghtalab, Joseph Naor, Nima Anari
2020 arXiv   pre-print
Robust submodular maximization has been proposed as a richer model that aims to overcome this discrepancy as well as increase the modeling scope of submodular optimization.  ...  In this work, we consider robust submodular maximization with structured combinatorial constraints and give efficient algorithms with provable guarantees.  ...  We also thank Shabbir Ahmed for the discussions about the distributionally robust problem (16).  ... 
arXiv:1710.04740v3 fatcat:3kaoks2l5vd5vp4mnar4mq4rqa

Adversarially Robust Submodular Maximization under Knapsack Constraints [article]

Dmitrii Avdiukhin, Slobodan Mitrović, Grigory Yaroslavtsev, Samson Zhou
2019 arXiv   pre-print
We propose the first adversarially robust algorithm for monotone submodular maximization under single and multiple knapsack constraints with scalable implementations in distributed and streaming settings  ...  For multiple knapsack constraints, our approximation is within a constant-factor of the best known non-robust solution.  ...  Streaming robust submodular maximization: A partitioned thresholding approach.  ... 
arXiv:1905.02367v1 fatcat:pu75pedrvzh63iiyz2hbbfqqsi

A distributed algorithm for partitioned robust submodular maximization

Ilija Bogunovic, Slobodan Mitrovic, Jonathan Scarlett, Volkan Cevher
2017 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)  
In this paper, we consider the problem of maximizing a monotone submodular function subject to a cardinality constraint, with two added twists: The computation is distributed across a number of machines  ...  We provide two versions of a partitioned robust algorithm for this problem, with the difference amounting to whether or not the centralized machine is informed (only in the final stage of the algorithm  ...  Related Work The two most related works in the literature are the distributed submodular maximization framework of [6] , and the robust framework of [10] .  ... 
doi:10.1109/camsap.2017.8313155 dblp:conf/camsap/BogunovicMSC17 fatcat:xm2tkhuv5nd3bjsh7k5zewdigi

Efficient algorithms for robust submodular maximization under matroid constraints [article]

Sebastian Pokutta and Mohit Singh and Alfredo Torrico
2018 arXiv   pre-print
In this work, we consider robust submodular maximization with matroid constraints.  ...  We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value.  ...  The initial model for robust submodular function maximization was introduced in Krause et al. (2008a) .  ... 
arXiv:1807.09405v1 fatcat:t47l2sohjfh7zcplh6jjo7sdpy

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
Through the above-mentioned link to the robust setting, both of these algorithms improve on the current state-of-the-art for robust submodular maximization, showing that approximation factors beyond 1/  ...  We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational  ...  Thus, it is deferred to Appendix A.1. Robust submodular function maximization.  ... 
arXiv:2003.13459v1 fatcat:dea4oconzraajf764fwnvolrl4

Mixed Robust/Average Submodular Partitioning: Fast Algorithms, Guarantees, and Applications to Parallel Machine Learning and Multi-Label Image Segmentation [article]

Kai Wei, Rishabh Iyer, Shengjie Wang, Wenruo Bai, Jeff Bilmes
2016 arXiv   pre-print
We study two mixed robust/average-case submodular partitioning problems that we collectively call Submodular Partitioning.  ...  (that is the submodular welfare problem (SWP) and submodular multiway partition (SMP).  ...  IIS-1162606, the National Institutes of Health under award R01GM103544, and by a Google, a Microsoft, and an Intel research award. R.  ... 
arXiv:1510.08865v2 fatcat:ttstqm3dy5fznci3s5qkwoor2e

Distributed Submodular Maximization [article]

Baharan Mirzasoleiman, Amin Karbasi, Rik Sarkar, Andreas Krause
2016 arXiv   pre-print
We begin with monotone submodular maximization subject to a cardinality constraint, and then extend this approach to obtain approximation guarantees for (not necessarily monotone) submodular maximization  ...  In this paper, we consider the problem of submodular function maximization in a distributed fashion.  ...  This suggests that our approach is quite robust, and may be more generally applicable. 6.4 Comparision with Greedy Scaling.  ... 
arXiv:1411.0541v2 fatcat:argsl5avqrdnzin64rype6xmmm

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)  
We first introduce a distributed algorithm for maximizing a submodular function with a matroid constraint.  ...  We then develop an algorithm for maximizing time-varying submodular functions under partition matroid constraints, which arises in sensor placement and data caching.  ...  Subsequent works considered submodular maximization under multiple matroid and knapsack constraints, as well as maximization of non-monotone submodular functions [4] .  ... 
doi:10.1109/wiopt.2015.7151103 dblp:conf/wiopt/ClarkABP15 fatcat:of4s2m4oknfi5aumuq2ahs4cem

Robust Influence Maximization

Wei Chen, Tian Lin, Zihan Tan, Mingfei Zhao, Xuren Zhou
2016 Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '16  
We further study uniform sampling and adaptive sampling methods to effectively reduce the uncertainty on parameters and improve the robustness of the influence maximization task.  ...  In this paper, we address the important issue of uncertainty in the edge influence probability estimates for the well studied influence maximization problem -the task of finding k seed nodes in a social  ...  Our RIM problem can be viewed as a specific instance of robust submodular optimization studied in [20] .  ... 
doi:10.1145/2939672.2939745 dblp:conf/kdd/ChenLTZZ16 fatcat:3cf5otw3nbhszier5sjhw7oq64

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  ...  In the case when influencing each user has uniform cost, the approximation becomes even better to a factor of 1/3.  ...  Influence Maximization with Non-Uniform Costs User-cost and product-budget generation.  ... 
arXiv:1312.2164v2 fatcat:s3yvg7awtnbfnm52zsjo5jznzy

Continuous Submodular Function Maximization [article]

Yatao Bian, Joachim M. Buhmann, Andreas Krause
2020 arXiv   pre-print
Continuous submodular functions are a category of generally non-convex/non-concave functions with a wide spectrum of applications.  ...  In this paper, we systematically study continuous submodularity and a class of non-convex optimization problems: continuous submodular function maximization.  ...  Ene and Nguyen (2016) provide an approach for reducing integer DR-submodular function maximization problems to submodular set function maximization problem.  ... 
arXiv:2006.13474v1 fatcat:aqlqnvv4qzfyxiydpficoeu55q

Robust Influence Maximization [article]

Wei Chen, Tian Lin, Zihan Tan, Mingfei Zhao, Xuren Zhou
2016 arXiv   pre-print
We further study uniform sampling and adaptive sampling methods to effectively reduce the uncertainty on parameters and improve the robustness of the influence maximization task.  ...  In this paper, we address the important issue of uncertainty in the edge influence probability estimates for the well studied influence maximization problem --- the task of finding k seed nodes in a social  ...  Our RIM problem can be viewed as a specific instance of robust submodular optimization studied in [19] .  ... 
arXiv:1601.06551v2 fatcat:pg7yijdthzgwzdomqr2l3jjvnu

Maximizing diversity over clustered data [chapter]

Guangyi Zhang, Aristides Gionis
2020 Proceedings of the 2020 SIAM International Conference on Data Mining  
We further extend the algorithm to the case of monotone and submodular quality function, and under a partition matroid constraint.  ...  Diversity under a uniform or partition matroid constraint naturally describes useful cardinality or budget requirements, and admits simple approximation algorithms [5] .  ...  As before we focus on monotone non-decreasing and submodular functions.  ... 
doi:10.1137/1.9781611976236.73 dblp:conf/sdm/ZhangG20 fatcat:3ndh6dlmhbgcbnwej7zmmxydha

Deletion Robust Submodular Maximization over Matroids [article]

Paul Dütting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Morteza Zadimoghaddam
2022
Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint.  ...  Here the goal is to extract a small size summary of the dataset that contains a high value independent set even after an adversary deleted some elements.  ...  Finally, note that the state-of-the-art for (non-robust) streaming submodular maximization with matroid constraint is a 3.147-approximation [Feldman et al., 2021] .  ... 
doi:10.48550/arxiv.2201.13128 fatcat:uar2ash3svezhnd75wvmtdxwvy
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