Complete Optimal Deployment Patterns for Full-Coverage and k-Connectivity (k ≦ 6) Wireless Sensor Networks Xiaole Bai, Dong Xuan, Ten H. Lai, Ziqiu Yun,

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Complete Optimal Deployment Patterns for Full-Coverage and k-Connectivity (k ≦ 6) Wireless Sensor Networks Xiaole Bai, Dong Xuan, Ten H. Lai, Ziqiu Yun, Weijia Jia Computer Science and Engineering The Ohio State University, USA Department of Mathematics Suzhou University, CHINA Department of Computer Science City University of Hong Kong, CHINA ACM International Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc 2008 YearSubmittedAccepted% Accepted % % %

Outline IntroductionThe proposed patternsNumerical resultsConclusion

Introduction Wireless sensor networks show more and more popularity for both military and civil applications.

Introduction Wireless sensor networks show more and more popularity for both military and civil applications. –Noxious Gas Detection

Introduction Wireless sensor networks show more and more popularity for both military and civil applications. –Fire Detection

The deployment is a fundamental issue in Wireless Sensor Networks (WSNs) that affects many facts for these applications. There are two categories of deployments in WSNs. –Random deployment –Deterministic deployment Introduction

RsRs

Achieve 6-connectivity only when r c ≧ RsRs A

The work on exploring optimal patterns in WSNs is not yet complete. –3-connected –5-connected –6-connected when R c / R s < The previous exploration on optimal patterns has not yet been conducted systematically. Introduction

Goal Propose deployment patterns systematically. –Achieve full coverage and k-connectivity (k ≦ 6) under different ratios of sensor communication range over sensing range.

Deployment Patterns Universal elemental patternk=3k=4k=5k=6 k=1 or k=2

Deployment Patterns - Universal elemental pattern θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s

Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=15, Rs=20 :  1 = 120 °,  2 = 120 °,  3 = 120 °, d 1 =15, d 2 =15 120° 15

Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=25, Rs=20 :  1 = °,  2 = °,  3 = °, d 1 =25, d 2 = ° ° ° ° 25

Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=28.284, Rs=20 :  1 = 180°,  2 = 90°,  3 = 90°, d 1 =28.284, d 2 = ° 90° 180°90°

Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 180°,  2 = °,  3 = 73.74°, d 1 = 32, d 2 = ° °73.74° 180° °73.74° 32

Deployment Patterns – 3-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=40, Rs=20 :  1 = 180°,  2 = 120°,  3 = 60°, d 1 = , d 2 = ° 120°60° 180° 120 °60°

Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s

Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s ≦ √2 √2 < R c / R s < √3 √3 ≦ R c / R s 180° 90° 180°90° RcRc RcRc RcRc RcRc RcRc RcRc

Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 180°,  2 = °,  3 = 73.74°, d 1 = 32, d 2 = ° °73.74° 180° °73.74° 32

Deployment Patterns – 4-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=40, Rs=20 :  1 = 180°,  2 = 120°,  3 = 60°, d 1 = , d 2 = ° 120°60° 180° 120 °60°

Deployment Patterns – 5-connectivity R c / R s ≦ √2 √2 < R c / R s < √3 √3 ≦ R c / R s θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

Deployment Patterns – 5-connectivity R c / R s ≦ √2 √2 < R c / R s < √3 √3 ≦ R c / R s 150° 60° 150° 60° RcRc RcRc RcRc RcRc RcRc RcRc θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

Deployment Patterns – 5-connectivity R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 60 °,  2 = °,  3 = °, d 1 = 32, d 2 = 32 60° ° ° 60° ° ° 32 θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

Deployment Patterns – 5-connectivity R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=40, Rs=20 :  1 = 60°,  2 = 180°,  3 = 120°, d 1 = , d 2 = ° 180° 120° 60° 180 ° 120° θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2

Deployment Patterns – 6-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < √3 √3 ≦ R c / R s

Deployment Patterns – 6-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 180° 120°60° 180° 120°60° RcRc RcRc RcRc RcRc RcRc RcRc R c / R s < √3 √3 ≦ R c / R s

Deployment Patterns – 6-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 180° 120°60° 180° 120°60° RsRs RsRs RsRs RsRs RsRs RsRs R c / R s < √3 √3 ≦ R c / R s

Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s

Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=15, Rs=20 :  1 = 180°,  2 =78.779°,  3 =101.22°, d 1 =15, d 2 = °78.779°101.22° 180°78.779°101.22°

Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=25, Rs=20 :  1 = 180°,  2 = °,  3 = °, d 1 =25, d 2 = °69.450°110.55° 180° °110.55°

Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=28.284, Rs=20 :  1 = 180°,  2 = 65.53°,  3 = °, d 1 =28.284, d 2 = °65.53°114.47° ° 180° 65.53°

Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=32, Rs=20 :  1 = 180°,  2 = 60°,  3 = 120°, d 1 = 32, d 2 = °60°120° ° 180° 60°

Deployment Patterns – 1 or 2-connectivity θ1θ1 θ1θ1 θ2θ2 θ2θ2 θ3θ3 θ3θ3 d1d1 d1d1 d1d1 d1d1 d2d2 d2d2 R c / R s < 1 1 ≦ R c / R s < √2 R c / R s = √2 √2 < R c / R s < √3 √3 ≦ R c / R s Rc=39, Rs=20 :  1 = 180°,  2 = °,  3 = °, d 1 = , d 2 = ° °142.91° ° 180° °

Deployment Patterns

Numerical Results Parameters SimulatorUnknow Size of network1000*1000 m Sensing range30 m Communication range20~60 m

Numerical Results

Conclusion This paper propose deployment patterns systematically. –Achieve full coverage and k-connectivity (k ≦ 6) under different ratios of sensor communication range over sensing range.