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Optimal Region Search with Submodular Maximization

Xuefeng Chen, Xin Cao, Yifeng Zeng, Yixiang Fang, Bin Yao
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Region search is an important problem in location-based services due to its wide applications. In this paper, we study the problem of optimal region search with submodular maximization (ORS-SM).  ...  We compute an objective value over the locations in the region using a submodular function and a budget value by summing up the costs of edges in the region, and aim to search the region with the largest  ...  We denote this problem as optimal region search with submodular maximization (ORS-SM).  ... 
doi:10.24963/ijcai.2020/169 dblp:conf/ijcai/Chen0ZFY20 fatcat:eljjluxupzgeplcxd3nflx7jz4

Constrained robust submodular sensor selection with application to multistatic sonar arrays

Thomas Powers, David W. Krout, Jeff Bilmes, Les Atlas
2017 IET radar, sonar & navigation  
We propose a novel algorithm called MatSat that exploits submodularity and, as a result, returns a near-optimal solution with approximation guarantees on a relaxed problem that are within a small factor  ...  In these ping sequence optimization simulations, MatSat exceeds the fractional lower bounds and reaches near-optimal performance, and submodular function optimization vastly outperforms traditional approaches  ...  MatSat and exhaustive search are optimized with respect to Equation(3.2), while SFO-Greedy is optimized with respect to Equation (3.1).  ... 
doi:10.1049/iet-rsn.2017.0075 fatcat:kyxt3ygqyzfmhose4fhokh2jsu

A topology optimization method for electric machines and devices through submodular maximization

Takahiro Sato, Masafumi Fujita
2019 Electronics and Communications in Japan  
This paper presents a topology optimization method using a greedy algorithm for submodular maximization. This method is based on a shape representation using the normalized Gaussian network.  ...  K E Y W O R D S greedy algorithm, submodular function, topology optimization Electron Comm Jpn. 2019;102:3-11.  ...  Proposal of more efficient optimization methods combining global search techniques with greedy algorithms for submodular maximization is a topic for further study.  ... 
doi:10.1002/ecj.12173 fatcat:jcgtn7t2tjavfjx3zz73l6njc4

An Approximation Algorithm for Risk-averse Submodular Optimization [article]

Lifeng Zhou, Pratap Tokekar
2018 arXiv   pre-print
We formulate a discrete submodular maximization problem for selecting a set using Conditional-Value-at-Risk (CVaR), a risk metric commonly used in financial analysis.  ...  While CVaR has recently been used in optimization of linear cost functions in robotics, we take the first stages towards extending this to discrete submodular optimization and provide several positive  ...  SGA gives 1/(1 + k f ) approximation of the optimal with two approximation errors. One approximation error comes from the searching separation ∆.  ... 
arXiv:1807.09358v2 fatcat:caj4mtr5hzggthub5wgl3l54ky

Risk-Aware Submodular Optimization for Multi-objective Travelling Salesperson Problem [article]

Rishab Balasubramanian, Lifeng Zhou, Pratap Tokekar, P.B. Sujit
2021 arXiv   pre-print
Unlike prior work, we focus on the scenario where the costs and the rewards are uncertain and seek to maximize the Conditional-Value-at-Risk (CVaR) metric of the submodular function.  ...  The approximation algorithm runs in polynomial time and is within a constant factor of the optimal and an additive term that depends on the optimal solution.  ...  delivery vehicle in dense urban regions with uncertain traffic, etc.  ... 
arXiv:2011.01095v2 fatcat:5fpegfwdtnd2ti474ng4xyvlne

Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints

Jon Lee, Vahab S. Mirrokni, Viswanath Nagarajan, Maxim Sviridenko
2010 SIAM Journal on Discrete Mathematics  
Unlike submodular minimization, submodular maximization is NP-hard.  ...  Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint  ...  Set function g is a submodular function on ground set U . Combined with (3.3) we obtain the claim. Local search for problem (3.2). Denote the region U := {y : 0 ≤ y i ≤ u i ∀i ∈ V }.  ... 
doi:10.1137/090750020 fatcat:fkozckgiyzgtriks4vti5uvbmu

Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms [chapter]

Tobias Friedrich, Frank Neumann
2014 Lecture Notes in Computer Science  
Many combinatorial optimization problems have underlying goal functions that are submodular.  ...  For the case of non-monotone submodular functions with k matroid intersection constraints, we show that GSEMO achieves a 1/(k + 2 + 1/k + ε)-approximation in expected time O(n k+5 log(n)/ε).  ...  feasible region of the problem.  ... 
doi:10.1007/978-3-319-10762-2_91 fatcat:l4na2rgmovcphl2aqnatrz3ko4

Maximizing Non-monotone Submodular Set Functions Subject to Different Constraints: Combined Algorithms [article]

Salman Fadaei, MohammadAmin Fazli, MohammadAli Safari
2016 arXiv   pre-print
The continuous greedy process has been previously used for maximizing smooth monotone submodular function over a down-monotone polytope CCPV08.  ...  We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity  ...  We want to maximize F over the region U : max{F (y) : y ∈ U } For this, we extend the 0.4-approximation algorithm (Smooth Local Search or SLS) of [FMV07] as follows. We call our algorithm F M V Y .  ... 
arXiv:1101.2973v5 fatcat:sjubtewxpbaqzhb4vchzbf5kve

Analysis and Augmentation of Human Performance on Telerobotic Search Problems

Kuo-Shih Tseng, Berenice Mettler
2020 IEEE Access  
Since the objective functions in search problems are submodular, greedy algorithms can generate near-optimal subgoals. These subgoals then can be used to guide humans in searching.  ...  Experiments showed that the humans' search performance is improved with the subgoals' assistance.  ...  If the constraint is cardinality cost (for all item cost is 1), the s is with the maximal submodular value.  ... 
doi:10.1109/access.2020.2981978 fatcat:bltvfi77ljf3poecnhtoiftykm

On the Unreasonable Effectiveness of the Greedy Algorithm: Greedy Adapts to Sharpness [article]

Alfredo Torrico, Mohit Singh, Sebastian Pokutta
2020 arXiv   pre-print
This improvement ties in closely with the faster convergence rates of first order methods for sharp functions in convex optimization.  ...  Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems.  ...  Search for submodular sharpness. Fix an optimal solution S * .  ... 
arXiv:2002.04063v1 fatcat:u5bypzyuxrbz5b2l27epyndfiy

On Submodular Search and Machine Scheduling [article]

Robbert Fokkink, Thomas Lidbetter, László A. Végh
2018 arXiv   pre-print
The cost of searching subsets of S is given by a submodular function and the probability that all objects are contained in a subset is given by a supermodular function.  ...  We go on to give better approximations for submodular functions with low total curvature and we give a full solution when the problem is what we call series-parallel decomposable.  ...  The authors would like to thank Christoph Dürr for pointing out the connection between expanding search and scheduling.  ... 
arXiv:1607.07598v4 fatcat:2sytqt4g2rhtpjtolq3kvffiuq

Efficient touch based localization through submodularity

Shervin Javdani, Matthew Klingensmith, J. Andrew Bagnell, Nancy S. Pollard, Siddhartha S. Srinivasa
2013 2013 IEEE International Conference on Robotics and Automation  
Many robotic systems deal with uncertainty by performing a sequence of information gathering actions.  ...  Our work first explains this high performance -we note a commonly used metric, reduction of Shannon entropy, is submodular under certain assumptions, rendering the greedy solution comparable to the optimal  ...  One class of problems known to perform well with a greedy strategy is submodular maximization.  ... 
doi:10.1109/icra.2013.6630818 dblp:conf/icra/JavdaniKBPS13 fatcat:pnfm62k2lbanpbulor273kogvu

Towards Scalable Voltage Control in Smart Grid: A Submodular Optimization Approach

Zhipeng Liu, Andrew Clark, Phillip Lee, Linda Bushnell, Daniel Kirschen, Radha Poovendran
2016 2016 ACM/IEEE 7th International Conference on Cyber-Physical Systems (ICCPS)  
In this paper, we propose a submodular optimization approach to designing a control strategy to prevent voltage instability at one or more buses.  ...  provable optimality guarantees.  ...  We demonstrated that the voltage control problem is equivalent to submodular maximization with a matroid basis constraint, leading to efficient approximation algorithms with provable optimality bounds.  ... 
doi:10.1109/iccps.2016.7479120 dblp:conf/iccps/LiuCLBKP16 fatcat:w3oklws46vbxfjxoip6k4gqmae

Maximizing Non-Monotone Submodular Functions

Uriel Feige, Vahab S. Mirrokni, Jan Vondrak
2007 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)  
In particular, we give a deterministic local-search 1 3 -approximation and a randomized 2 5 -approximation algorithm for maximizing nonnegative submodular functions.  ...  Unlike the problem of minimizing submodular functions, the problem of maximizing submodular functions is NP-hard.  ...  We thank Maxim Sviridenko for pointing out related work.  ... 
doi:10.1109/focs.2007.29 dblp:conf/focs/FeigeMV07 fatcat:cxjp34elk5fm3hgxckwgizehwm

Submodular Maximization with Nearly Optimal Approximation, Adaptivity and Query Complexity [article]

Matthew Fahrbach, Vahab Mirrokni, Morteza Zadimoghaddam
2018 arXiv   pre-print
Our main result is a distributed algorithm for maximizing a monotone submodular function with cardinality constraint k that achieves a (1-1/e-ε)-approximation in expectation.  ...  Motivated by these applications, we study the adaptivity and query complexity of adaptive submodular optimization.  ...  Next, modify and run Exhaustive-Maximization(f, k,ε,ε) so that it searches over the interval with ratio O(ε −2 ).  ... 
arXiv:1807.07889v2 fatcat:szcpe6gvhfaozjpcmuunnzfr2e
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