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Generalized submodular cover problems and applications

Judit Bar-Ilan, Guy Kortsarz, David Peleg
2001 Theoretical Computer Science  
The problems for which these conditions hold are known as submodular cover problems. The current paper 3 extends the applicability of the greedy approach to wider classes of problems.  ...  The second type involves some (known and new) center selection problems, for which new logarithmic ratio approximation algorithms are given.  ...  It is easily seen that this problem generalizes the set cover problem.  ... 
doi:10.1016/s0304-3975(99)00130-9 fatcat:zbhiiwz7wreutex65zjplenbui

Approximability of Combinatorial Problems with Multi-agent Submodular Cost Functions

Gagan Goel, Chinmay Karande, Pushkar Tripathi, Lei Wang
2009 2009 50th Annual IEEE Symposium on Foundations of Computer Science  
We study several fundamental covering problems in this framework and establish upper and lower bounds on their approximability.  ...  In this paper, we introduce an algorithmic framework for studying combinatorial optimization problems in the presence of multiple agents with submodular cost functions.  ...  Combinatorial Problems with Multiple agents · 3 Motivation and Applications From a practical viewpoint, each of the problems we study is meaningful in its own right.  ... 
doi:10.1109/focs.2009.81 dblp:conf/focs/GoelKTW09 fatcat:edkhlmryjfcwxbmogqekq4psqi

Approximability of combinatorial problems with multi-agent submodular cost functions

Gagan Goel, Chinmay Karande, Pushkar Tripathi, Lei Wang
2010 ACM SIGecom Exchanges  
We study several fundamental covering problems in this framework and establish upper and lower bounds on their approximability.  ...  In this paper, we introduce an algorithmic framework for studying combinatorial optimization problems in the presence of multiple agents with submodular cost functions.  ...  Combinatorial Problems with Multiple agents · 3 Motivation and Applications From a practical viewpoint, each of the problems we study is meaningful in its own right.  ... 
doi:10.1145/1980534.1980542 fatcat:aecxybef7zbzhpm5alfd7siqfm

Submodular Functions: Optimization and Approximation

Satoru Iwata
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
problems with submodular costs.  ...  On the other hand, for submodular function maximization, which is NP-hard and known to refuse any polynomial algorithms, constant factor approximation algorithms have been developed with applications to  ...  It is a natural attempt to replace linear functions in combinatorial optimization problems with submodular functions to obtain a more general results applicable to a wide variety of problems.  ... 
doi:10.1142/9789814324359_0173 fatcat:uspd2ma2uzco3kvzqiytgxz45a

Interactive Submodular Set Cover [article]

Andrew Guillory, Jeff Bilmes
2010 arXiv   pre-print
We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover.  ...  Applications include advertising in social networks with hidden information.  ...  Future Work We believe there are other interesting applications which can be posed as interactive submodular set cover.  ... 
arXiv:1002.3345v2 fatcat:mxhdvr2bfnfpxcuwud5rk5bltq

Submodular Combinatorial Information Measures with Applications in Machine Learning [article]

Rishabh Iyer and Ninad Khargonkar and Jeff Bilmes and Himanshu Asnani
2021 arXiv   pre-print
Regarding applications, we connect the maximization of submodular (conditional) mutual information to problems such as mutual-information-based, query-based, and privacy-preserving summarization -- and  ...  This turns out to include a number of practically useful cases such as the facility location and set-cover functions.  ...  This paper provides a complete picture of the combinatorial information measures defined via general submodular functions, by studying various properties, examples, optimization problems, and applications  ... 
arXiv:2006.15412v6 fatcat:ns3ctxnkovdgbo66awqimjzjuy

Submodular Optimization with Submodular Cover and Submodular Knapsack Constraints [article]

Rishabh Iyer, Jeff Bilmes
2013 arXiv   pre-print
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular  ...  We are motivated by a number of real-world applications in machine learning including sensor placement and data subset selection, which require maximizing a certain submodular function (like coverage or  ...  (IIS-1162606) , a Google and a Microsoft award, and by the Intel Science and Technology Center for Pervasive Computing.  ... 
arXiv:1311.2106v1 fatcat:3jmjw4cus5djxaa63ppvuhp3ai

Submodular game for distributed application allocation in shared sensor networks

Chengjie Wu, You Xu, Yixin Chen, Chenyang Lu
2012 2012 Proceedings IEEE INFOCOM  
We first transform the optimal application allocation problem to a submodular game and then develop a decentralized algorithm that only employs localized interactions among neighboring nodes.  ...  Recent solutions to this challenging application allocation problem are centralized in nature, limiting their scalability and robustness against network failures and dynamics.  ...  Application Allocation Problem Formulation Given QoM metric as covariance cover, we want to further formulate the application allocation problem in shared sensor networks.  ... 
doi:10.1109/infcom.2012.6195490 dblp:conf/infocom/WuXCL12 fatcat:3wz6suff45buxjoaqzwv6s3pke

Adaptive Submodular Ranking and Routing [article]

Fatemeh Navidi, Prabhanjan Kambadur, Viswanath Nagarajan
2019 arXiv   pre-print
This problem unifies and generalizes many previously studied problems with applications in search ranking and active learning.  ...  This routing problem is a significant generalization of the previously-studied adaptive traveling salesman and traveling repairman problems.  ...  The authors thank Lisa Hellerstein for a clarification on [24] regarding the OR construction of submodular functions.  ... 
arXiv:1606.01530v2 fatcat:e4lnyl63indcjnpgeuadu6xyfe

Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization [article]

Daniel Golovin, Andreas Krause
2017 arXiv   pre-print
Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.  ...  In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies.  ...  We wish to thank Vitaly Feldman and Jan Vondrák for providing an elegant proof of Lemma 47.  ... 
arXiv:1003.3967v5 fatcat:hwhqn5vvjfb25omq646qcimsay

Maximizing submodular set function with connectivity constraint: Theory and application to networks

Tung-Wei Kuo, Kate Ching-Ju Lin, Ming-Jer Tsai
2013 2013 Proceedings IEEE INFOCOM  
However, this deployment problem is more difficult than the traditional maximum submodular set function problem, e.g., the maximum coverage problem, because it requires all the deployed routers to form  ...  We found that many goals for network deployment, such as maximizing the number of covered users or areas, or the total throughput of the network, can be modelled with the submodular set function.  ...  We investigate several potential applications in wireless networks and show that these problems are special cases of the maximum connected submodular set function problem discussed in this paper.  ... 
doi:10.1109/infcom.2013.6566998 dblp:conf/infocom/KuoLT13 fatcat:7c7mjvu6ebbsdkol2iduqb2s3a

Submodularity in Action: From Machine Learning to Signal Processing Applications [article]

Ehsan Tohidi, Rouhollah Amiri, Mario Coutino, David Gesbert, Geert Leus, Amin Karbasi
2020 arXiv   pre-print
problems are encountered in a wide range of applications.  ...  We introduce a variety of submodular-friendly applications, and elucidate the relation of submodularity to convexity and concavity which enables efficient optimization.  ...  Moreover, several applications in SP and ML have been covered to transfer the flavor of submodularity to practice.  ... 
arXiv:2006.09905v1 fatcat:ksn2bqbdczechktpa6ivcpwcau

Adaptive Submodular Ranking [chapter]

Prabhanjan Kambadur, Viswanath Nagarajan, Fatemeh Navidi
2017 Lecture Notes in Computer Science  
This problem unifies and generalizes many previously studied problems with applications in search ranking and active learning.  ...  We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected  ...  The authors thank Lisa Hellerstein for a clarification on [16] regarding the OR construction of submodular functions.  ... 
doi:10.1007/978-3-319-59250-3_26 fatcat:xjsdp423nvbedoz6jzdsu7snju

Maximizing Submodular Set Function With Connectivity Constraint: Theory and Application to Networks

Tung-Wei Kuo, Kate Ching-Ju Lin, Ming-Jer Tsai
2015 IEEE/ACM Transactions on Networking  
However, this deployment problem is more difficult than the traditional maximum submodular set function problem, e.g., the maximum coverage problem, because it requires all the deployed routers to form  ...  We found that many goals for network deployment, such as maximizing the number of covered users or areas, or the total throughput of the network, can be modelled with the submodular set function.  ...  We investigate several potential applications in wireless networks and show that these problems are special cases of the maximum connected submodular set function problem discussed in this paper.  ... 
doi:10.1109/tnet.2014.2301816 fatcat:lim42y3kpndrnpvshhwyp737oy

A Memoization Framework for Scaling Submodular Optimization to Large Scale Problems [article]

Rishabh Iyer, Jeff Bilmes
2019 arXiv   pre-print
optimization, optimization with submodular constraints and several other related optimization problems.  ...  We show that we can easily integrate this idea into a large class of submodular optimization problems including constrained and unconstrained submodular maximization, minimization, difference of submodular  ...  We show how several real world submodular functions admit natural precompute statistics, and how we can integrate this idea into a large family of algorithms for submodular maximization, minimization and  ... 
arXiv:1902.10176v1 fatcat:v2vicnn7ofhnzjltctumqjorda
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