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Optimal Region Search with Submodular Maximization
2020
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
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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
2017
IET radar, sonar & navigation
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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
2019
Electronics and Communications in Japan
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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]
2018
arXiv
pre-print
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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]
2021
arXiv
pre-print
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2020 pre-print arXiv:2011.01095v1 fatcat:gqhdn6x6tnbtzbswdircxghuli
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
2010
SIAM Journal on Discrete Mathematics
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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]
2014
Lecture Notes in Computer Science
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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]
2016
arXiv
pre-print
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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
2020
IEEE Access
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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]
2020
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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
2013
2013 IEEE International Conference on Robotics and Automation
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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
2016
2016 ACM/IEEE 7th International Conference on Cyber-Physical Systems (ICCPS)
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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
2007
48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)
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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]
2018
arXiv
pre-print
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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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