## Complete Optimal Deployment Patterns for Full-Coverage and k−Connectiviy (k ≤ 6) Wireless Sensor Networks (2008)

### Cached

### Download Links

Venue: | In Proc. of ACM MobiHoc |

Citations: | 23 - 7 self |

### BibTeX

@INPROCEEDINGS{Bai08completeoptimal,

author = {Xiaole Bai and Dong Xuan and Ziqiu Yun and Ten H. Lai and Weijia Jia},

title = {Complete Optimal Deployment Patterns for Full-Coverage and k−Connectiviy (k ≤ 6) Wireless Sensor Networks},

booktitle = {In Proc. of ACM MobiHoc},

year = {2008}

}

### OpenURL

### Abstract

Abstract—In this paper, we study deployment patterns to achieve full coverage and k-connectivity (k ≤ 6) under different ratios of the sensor communication range (denoted by Rc) to the sensing range (denoted by Rs) for homogeneous wireless sensor networks (WSNs). In particular, we propose new patterns for 3- and 5-connectivity. We also discover that there exists a hexagon-based universally elemental pattern that can generate all known optimal patterns. The previously proposed Voronoibased approach can not be applied to prove the optimality of the new patterns due to their special features. We propose a new deployment-polygon based methodology. We prove the optimality of deployment patterns to achieve three-connectivity, fourconnectivity and five-connectivity for certain ranges of Rc/Rs, respectively, and prove the optimality of deployment patterns to achieve six-connectivity under all ranges of Rc/Rs.

### Citations

1767 | Wireless Communications: Principles and Practice - Rappaport - 1996 |

219 | et al., “A line in the sand: A wireless sensor network for target detection, classification,and tracking
- Arora, Dutta, et al.
- 2004
(Show Context)
Citation Context ...le) in missions when the deployment area is physically accessible. Missions in which WSNs are deterministically deployed are becoming increasingly popular today. Examples include the Line in the Sand =-=[2]-=- sensor network for target tracking, the CitySense [18] network for urban monitoring, the Soil Monitoring [6] sensor network, etc., where sensors are placed by hand at selected spots prior to network ... |

204 | Approximation schemes for covering and packing problems in image processing and VLSI - Hochbaum, Maass - 1985 |

174 | On k-coverage in a mostly sleeping sensor network
- Kumar, TH, et al.
- 2004
(Show Context)
Citation Context ...or is capable of communicating only with others within distance Rc. Disc model for both sensing and communication that provides a good abstraction from the real world has been widely adopted, e.g. in =-=[3]-=-–[5], [7], [8]. We study the asymptotical optimality of deployment patterns, that is, a relatively large area compared with sensing and communication ranges is considered in this paper. The boundary e... |

170 | Analyzing the Transition Region in Low Power Wireless Links
- Zuniga, Krishnamachari
- 2004
(Show Context)
Citation Context ...ication Model: In reality, the communication wireless signal undergoes attenuation and various disruptive physical phenomena. We consider a widely used model suggested by Zuniga and Krishnamachari in =-=[21]-=-. This model established the function of the distance between the transmitter and the Fig. 1. Two examples of regular deployments. Solid lines denote the established communication links . In (a), each... |

117 | et al. Exscal: Elements of an extreme scale wireless sensor network
- Arora
- 2005
(Show Context)
Citation Context ...positive number. For example, while the reliable communication range of the Extreme Scale Mote platform is 30 m, the sensing range of the acoustics sensor for detecting an All Terrain Vehicle is 55 m =-=[1]-=-. In this case, Rc/Rs √ is much less than 3. Progress has been made in exploring optimal patterns under different values of Rc/Rs in recent years. In 2005, researchers proved that the strip-based depl... |

103 | Deploying Wireless Sensors to Achieve Both Coverage and Connectivity
- Bai, Kumary, et al.
- 2006
(Show Context)
Citation Context ...oyment pattern is asymptotically nearly optimal when Rc = Rs [5]. In 2006, the asymptotic optimality of strip-based deployment pattern to achieve one and two connectivity and full coverage was proved =-=[7]-=-. Furthermore, in a paper presented at Infocom 2008 [8], the asymptotically optimal pattern to achieve fourconnectivity and full coverage is explored. With the above progress, two questions naturally ... |

90 |
The Number of Circles Covering a Set
- Kershner
- 1939
(Show Context)
Citation Context ... problem is related to the covering problem in computational geometry. Much work has been done on the issue of covering points in a plane using a minimum number of given geometric bodies, e.g., disks =-=[10]-=-–[13], orthogonal rectangles [14], fat convex bodies [15], [16], etc. However, the literature in computational geometry only considers coverage, not connectivity. This is understandable as connectivit... |

77 | Topology control meets SINR: the scheduling complexity of arbitrary topologies
- Moscibroda, Wattenhofer, et al.
- 2006
(Show Context)
Citation Context ...g range of passive infrared (PIR) sensor roughly follows two dimensional Gaussian distribution. Studies have also suggested that wireless communication links could be irregular and being non-disc. In =-=[10]-=-, Moscibroda et al. propose the SINR model which implies that a receiver may not be able to receive signals correctly even when it is close to the sender because of interference and noise effects. The... |

69 | Barrier coverage with wireless sensors - Kumar, Lai, et al. |

57 | Improved approximation algorithms for geometric set cover
- Clarkson, Varadarajan
(Show Context)
Citation Context ...nal geometry. Much work has been done on the issue of covering points in a plane using a minimum number of given geometric bodies, e.g., disks [10]–[13], orthogonal rectangles [14], fat convex bodies =-=[15]-=-, [16], etc. However, the literature in computational geometry only considers coverage, not connectivity. This is understandable as connectivity is a typical networking requirement that is out of pure... |

49 | Analysis of target detection performance for wireless sensor networks
- Cao, Yan, et al.
(Show Context)
Citation Context ...nications models: In practice, the disc models do not always coincide empirical observations. It is suggested the quality of sensing could gradually attenuate with increasing distances. Cao et al. in =-=[5]-=- suggest the sensing range of passive infrared (PIR) sensor roughly follows two dimensional Gaussian distribution. Studies have also suggested that wireless communication links could be irregular and ... |

35 | Lowcoordination Topologies for Redundancy in Sensor Networks
- Iyengar, Kar, et al.
- 2005
(Show Context)
Citation Context ...n made in exploring optimal patterns under different values of Rc/Rs in recent years. In 2005, researchers proved that the strip-based deployment pattern is asymptotically nearly optimal when Rc = Rs =-=[5]-=-. In 2006, the asymptotic optimality of strip-based deployment pattern to achieve one and two connectivity and full coverage was proved [7]. Furthermore, in a paper presented at Infocom 2008 [8], the ... |

31 |
Covering a set of points in multidimensional space
- Gonzalez
- 1991
(Show Context)
Citation Context ...ng problem in computational geometry. Much work has been done on the issue of covering points in a plane using a minimum number of given geometric bodies, e.g., disks [10]–[13], orthogonal rectangles =-=[14]-=-, fat convex bodies [15], [16], etc. However, the literature in computational geometry only considers coverage, not connectivity. This is understandable as connectivity is a typical networking require... |

16 | Deploying Four-Connectivity And Full-Coverage Wireless Sensor Networks. (available on line) accepted by
- Bai, Yun, et al.
- 2008
(Show Context)
Citation Context ...tripe-based patterns for 1- and 2-connectivity. However, these patterns as well as those for 5-, 6-connectivity can solve the long path problem existing in the the stripe-based patterns, as stated in =-=[8]-=-. − For all Rc/Rs, the sensor number needed for the pattern achieving 5-connectivity is roughly the average of the number needed for 4- and 6-connectivity. It is 93% of the number for 6-connectivity. ... |

16 | Covering a square with up to 30 equal circles
- Nurmela, Ostergard
- 2000
(Show Context)
Citation Context ...lem is related to the covering problem in computational geometry. Much work has been done on the issue of covering points in a plane using a minimum number of given geometric bodies, e.g., disks [10]–=-=[13]-=-, orthogonal rectangles [14], fat convex bodies [15], [16], etc. However, the literature in computational geometry only considers coverage, not connectivity. This is understandable as connectivity is ... |

13 | Improved coverings of a square with six and eight equal circles - Melissen, Schuur - 1996 |

10 |
Sensor Deployment and Target Localization Based on Virtual Force
- Zhou, Charkrabarty
- 2003
(Show Context)
Citation Context ... , where λ and α are sensor dependent parameters and d is the distance between the sensor and detection target. In this model, the quality of sensing gradually attenuates with increasing distance. In =-=[20]-=-, Y. Zhou et al. propose a probabilistic sensing model. In this model, two values R1 and R2 (R1 ≤ R2) are defined from empirical observations. When the distance from the target to the sensor is less t... |

9 |
Covering with fat convex discs
- TOTH
- 2005
(Show Context)
Citation Context ...ometry. Much work has been done on the issue of covering points in a plane using a minimum number of given geometric bodies, e.g., disks [10]–[13], orthogonal rectangles [14], fat convex bodies [15], =-=[16]-=-, etc. However, the literature in computational geometry only considers coverage, not connectivity. This is understandable as connectivity is a typical networking requirement that is out of pure mathe... |