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Minimum-cost coverage of point sets by disks

Helmut Alt, Esther M. Arkin, Hervé Brönnimann, Jeff Erickson, Sándor P. Fekete, Christian Knauer, Jonathan Lenchner, Joseph S. B. Mitchell, Kim Whittlesey
2006 Proceedings of the twenty-second annual symposium on Computational geometry - SCG '06  
We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t j ) and radii (r j ) that cover a given set of demand points Y ⊂  ...  for the set of disks and the length of a tour/path that connects the centers of the disks.  ...  Acknowledgments We thank all of the participants of the McGill-INRIA International Workshop on Limited Visibility, at the Bellairs Research Institute of McGill University, where this research was originated  ... 
doi:10.1145/1137856.1137922 dblp:conf/compgeom/AltABEFKLMW06 fatcat:6uhhchoxgfe3xmuwaoysvvzimm

Minimum-Cost Coverage of Point Sets by Disks [article]

Esther M. Arkin and Herve Broennimann and Jeff Erickson and Sandor P. Fekete and Christian Knauer and Jonathan Lenchner and Joseph S. B. Mitchell and Kim Whittlesey
2006 arXiv   pre-print
We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t_j) and radii (r_j) that cover a given set of demand points Y in  ...  cost for the set of disks and the length of a tour/path that connects the centers of the disks.  ...  Acknowledgments We thank all of the participants of the McGill-INRIA International Workshop on Limited Visibility, at the Bellairs Research Institute of McGill University, where this research was originated  ... 
arXiv:cs/0604008v1 fatcat:grz5seta6nekvi6haficgl4sn4

A Note on Minimum-Sum Coverage by Aligned Disks [article]

Chan-Su Shin
2012 arXiv   pre-print
In this paper, we consider a facility location problem to find a minimum-sum coverage of n points by disks centered at a fixed line.  ...  The goal is to find a set of disks under Lp metric such that the disks are centered on the x-axis, their union covers n points, and the sum of the cost of the disks is minimized.  ...  When α = 1, the smallest disk containing all points is the optimal coverage. However, we can easily show for α > 1 that infinitely many disks always guarantee the minimum cost coverage for any input.  ... 
arXiv:1202.4821v3 fatcat:r27hjtijonhhfjxceecevayqky

Maximising lifetime for fault-tolerant target coverage in sensor networks

Thomas Erlebach, Tom Grant, Frank Kammer
2011 Sustainable Computing: Informatics and Systems  
Our algorithm for the minimum-weight fault-tolerant sensor cover problem generalises previous approximation algorithms for geometric set cover with weighted unit disks and is obtained by enumerating properties  ...  We study the problem of maximising the lifetime of a sensor network for fault-tolerant target coverage in a setting with composite events.  ...  the problem of covering all event points by sensors of minimum total cost.  ... 
doi:10.1016/j.suscom.2011.05.005 fatcat:p3de3prpezbspl5tyodwqrolyu

Maximising lifetime for fault-tolerant target coverage in sensor networks

Thomas Erlebach, Tom Grant, Frank Kammer
2011 Proceedings of the 23rd ACM symposium on Parallelism in algorithms and architectures - SPAA '11  
Our algorithm for the minimum-weight fault-tolerant sensor cover problem generalises previous approximation algorithms for geometric set cover with weighted unit disks and is obtained by enumerating properties  ...  We study the problem of maximising the lifetime of a sensor network for fault-tolerant target coverage in a setting with composite events.  ...  the problem of covering all event points by sensors of minimum total cost.  ... 
doi:10.1145/1989493.1989521 dblp:conf/spaa/ErlebachGK11 fatcat:ts33ownhana63bs7rmd5ox77xu

Minimum Shared-Power Edge Cut [article]

Sergio Cabello, Kshitij Jain, Anna Lubiw, Debajyoti Mondal
2018 arXiv   pre-print
MSPEC is a graph generalization of a barrier coverage problem in a wireless sensor network: given a set of unit disks with centers in a rectangle, what is the minimum total amount by which we must shrink  ...  This is a more sophisticated measure of barrier coverage than the minimum number of disks whose removal breaks the barrier. We develop a fully polynomial time approximation scheme (FPTAS) for MSPEC.  ...  Given a set of n points P in R 2 , the unit disk graph induced by P , denoted UDG(P ), is an embedded graph with vertex set P and an edge (u, v) when the unit disks centered at u and v intersect, i.e.,  ... 
arXiv:1806.04742v1 fatcat:v5sswugk3fdnjbad3n5dtnljxy

Distributed Gateway Placement for Cost Minimization in Wireless Mesh Networks

XiaoHua Xu, ShaoJie Tang, Xufei Mao, Xiang-Yang Li
2010 2010 IEEE 30th International Conference on Distributed Computing Systems  
We are given a set of mesh routers, assume they have identical transmission range r, represented by unit transmission disks around them. A router may be selected as a gateway at certain placing cost.  ...  The goal of this work is to select a set of mesh routers as gateways to serve the rest routers with minimum overall cost. This problem is NP-hard.  ...  problem of selecting a minimum set of sensors which are connected and each point in a target region is covered by at least k distinct sensors.  ... 
doi:10.1109/icdcs.2010.51 dblp:conf/icdcs/XuTML10 fatcat:roi4bm5ixrethnxz2k7qibdmza

Polynomial Algorithm for Node Deployment in Hybrid Wireless Sensor Networks

Lili Zhang, Jing Yuan, Yingchi Mao, Xiwei Zhang, Guihai Chen
2011 International Journal of Wireless and Microwave Technologies  
It is well known that the mobility of sensor nodes can improve the coverage and the probability of the detecting, so we deal with the problem of detecting a target using hybrid sensor networks which contain  ...  Then, one polynomial algorithm for node deployment in hybrid wireless sensor networks is proposed, which aims at minimizing the number of all sensors to reduce the cost.  ...  Acknowledgment (Heading 5) This work is supported in part by the China NSF grants (  ... 
doi:10.5815/ijwmt.2011.03.02 fatcat:ncqeu25mavgjnk6lchtoq6u7fu

Using Rotatable and Directional (R&D) Sensors to Achieve Temporal Coverage of Objects and Its Surveillance Application

You-Chiun Wang, Yung-Fu Chen, Yu-Chee Tseng
2012 IEEE Transactions on Mobile Computing  
Then, motivated by the system, we formulate an R&D sensor deployment problem, which tries to deploy the minimum number of R&D sensors to cover a given set of objects such that each object is covered by  ...  Due to hardware design or cost consideration, sensors may possess sector-like sensing coverage. Furthermore, by stepper motors, sensors can rotate to cover the objects around them.  ...  Given a set of point-locations, GDC asks how to find the minimum number of disks to cover all point-locations.  ... 
doi:10.1109/tmc.2011.161 fatcat:eak2kqcgwnainllgcjao3yvuwy

On Isolating Points Using Disks [article]

Matt Gibson, Gaurav Kanade, Kasturi Varadarajan
2011 arXiv   pre-print
of these points that is not intercepted by some disk.  ...  We try to achieve this separation using a minimum number of a given set of unit disks.  ...  We thank Alon Efrat for discussions that led to the formulation of the problem, and Sariel Har-Peled for discussions that led to the algorithm described here.  ... 
arXiv:1104.5043v2 fatcat:lruvgbfwvfb4hbvznu7vn7cjw4

Target Coverage in Wireless Sensor Networks with Probabilistic Sensors

Anxing Shan, Xianghua Xu, Zongmao Cheng
2016 Sensors  
We analyze the joint detection probability of target with multiple sensors. Based on the theoretical analysis of the detection probability, we formulate the minimum -detection coverage problem.  ...  We prove that the minimum -detection coverage problem is NP-hard and present an approximation algorithm called the Probabilistic Sensor Coverage Algorithm (PSCA) with provable approximation ratios.  ...  Acknowledgments: This work is supported by National Science Foundation of China (61370087), the Zhejiang Provincial Science and Technology Project (2013E60005, 2014C01044).  ... 
doi:10.3390/s16091372 pmid:27618902 pmcid:PMC5038650 fatcat:l4xci26mobcf5ouppsx4tklnbu

Wireless coverage with disparate ranges

Peng-Jun Wan, Xiaohua Xu, Zhu Wang
2011 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing - MobiHoc '11  
Given a set of nodes and a set of disks of disparate radii, the problem Minimum Disk Cover seeks a disk cover of all nodes with minimum cardinality.  ...  We also consider a classical generalization where each input disk is associated with a positive cost, the problem Min-Cost Disk Cover seeks a disk cover of all nodes with minimum total cost.  ...  We further consider a classical generalization where each disk is associated with a positive cost, the problem Min-Cost Disk Cover (MCDC) seeks a minimum cost disk cover D ′ ⊆ D of P.  ... 
doi:10.1145/2107502.2107517 dblp:conf/mobihoc/WanXW11 fatcat:jzxdbfr2xbhvrohr34divw5ib4

Faster Algorithms for some Optimization Problems on Collinear Points

Ahmad Biniaz, Prosenjit Bose, Paz Carmi, Anil Maheshwari, Ian Munro, Michiel Smid, Marc Herbstritt
2018 International Symposium on Computational Geometry  
The goal is to find a set of disks of minimum total area, covering I, such that every disk contains at least one input point. We present an algorithm that solves this problem in O(n 2 ) time.  ...  Minimizing sum of the radii of client-server coverage: The n points are partitioned into two sets, namely clients and servers.  ...  The point-interval coverage problem is to find such a set of disks with minimum total area.  ... 
doi:10.4230/lipics.socg.2018.8 dblp:conf/compgeom/BiniazBCMMS18 fatcat:h5vbrd5yhfgcxdzq2zzydvxolq

Line sweep coverage in wireless sensor networks

Barun Gorain, Partha Sarathi Mandal
2014 2014 Sixth International Conference on Communication Systems and Networks (COMSNETS)  
In this paper we have proposed a 2-approximation algorithm for solving the sweep coverage for a given set of points of interest (PoI). The best known approximation factor is 3 for this problem [11] .  ...  Finding minimum number of mobile sensor nodes with a constant velocity to guarantee sweep coverage is NP-hard and it cannot be approximated within a factor of 2 [11].  ...  The authors proved that finding minimum number of mobile sensor nodes to sweep coverage a set of discrete points is NP-complete.  ... 
doi:10.1109/comsnets.2014.6734885 dblp:conf/comsnets/GorainM14 fatcat:cbbw5qdnafapvdknv5qwmdiipe

The coverage problem for loitering Dubins vehicles

Ketan Savla, Francesco Bullo, Emilio Frazzoli
2007 2007 46th IEEE Conference on Decision and Control  
We do this by establishing an analogy to the disk covering problem.  ...  Given a compact region and a group of Dubins vehicles, the coverage problem is to minimize the worst-case traveling time from any vehicle to any point in the region.  ...  The coverage cost gives the worst-case traveling time from any vehicle to any point in the region. In the rest of the paper, we will use coverage cost and cost interchangeably.  ... 
doi:10.1109/cdc.2007.4435017 dblp:conf/cdc/SavlaBF07 fatcat:pl2mzs3wuvh4bkyeokrtsdiab4
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