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Geosensor Networks, Formal Foundations

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  • First Online:
Encyclopedia of GIS

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Synonyms

Mathematical theory of geosensor networks; Provable properties; Theoretical analysis

Definition

The geometric nature of geosensor networks (GSNs) has sparked an interest in researching their formal foundations. As the research on formal foundations has just begun, there is no single view of what encompasses a theoretical approach to sensor networks. Typically, a theoretical approach applies techniques from computational geometry, theoretical computer science, or mathematics, in particular (algebraic) topology and graph theory. The goal of a formal analysis is to identify fundamental properties of a sensor network, for example, the total number of sensors required if every point in the sensor field has to be covered by a fixed minimum number of sensors. More generally, a formal analysis studies provable properties of GSNs and algorithms used for GSNs. A formal analysis can compute the computational complexity of an algorithm and decide, if a problem has an efficient solution or...

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  • Berg M, Kreveld M, Overmars M, Schwarzkopf O (2000) Computational geometry: algorithms and applications. Springer, New York

    Book  MATH  Google Scholar 

  • Bose P, Morin P, Stojmenovic I, Urrutia J (2001) Routing with guaranteed delivery in ad hoc wireless networks. Wirel Netw 7:609–616

    Article  MATH  Google Scholar 

  • Cardei M, Wu J (2004) Coverage in wireless sensor networks. In: Ilyas M, Magboub I (eds) Handbook of sensor networks: compact wireless and wired sensing systems. CRC, Boca Raton, pp 19:1–19:10

    Google Scholar 

  • Diaz J, Penrose M, Petit J, Serna M (2000) Convergence theorems for some layout measures on random lattice and random geometric graphs. Comb Probab Comput 9:489–511

    Article  MathSciNet  MATH  Google Scholar 

  • Duckham M, Nittel S, Worboys M (2005) Monitoring dynamic spatial fields using responsive geosensor networks. In: GIS ’05: proceedings of the 13th annual ACM international workshop on geographic information systems, Bremen, 4–5 Nov 2005

    Google Scholar 

  • Gallager R, Humblet P, Spira P (1983) A distributed algorithm for minimum weight spanning trees. ACM Trans Program Lang Syst 5:66–77

    Article  MATH  Google Scholar 

  • Ghrist R, Muhammad A (2005) Coverage and hole-detection in sensor networks via homology. In: Proceedings of the 4th international symposium on information processing in sensor networks, Los Angeles, 25–27 Apr 2005

    Google Scholar 

  • Gupta P, Kumar P (2000) The capacity of wireless networks. IEEE Trans Inf Theory 46:388–404

    Article  MathSciNet  MATH  Google Scholar 

  • Karp B, Kung H (2000) GPSR: greedy perimeter stateless routing for wireless networks. In: Proceedings of the 6th international conference on mobile computing and networking, Boston, 6–11 Aug 2000

    Google Scholar 

  • Krishnamachari B, Estrin D, Wicker S (2002) The impact of data aggregation in wireless sensor networks. In: Proceedings of the 22nd international conference on distributed computing systems, workshops, Vienna, 2–5 July 2002

    Google Scholar 

  • Kuhn F, Wattenhofer R, Zhang Y, Zollinger A (2003) Geometric ad-hoc routing: of theory and practice. In: PODC ’03: proceedings of the 22nd annual symposium on principles of distributed computing, Boston, 13–16 July 2003

    Google Scholar 

  • Kulik L, Tanin E, Umer M (2007, in press) Efficient data collection and selective queries in sensor networks. In: Nittel S, Labrinidis A, Stefanidis A (eds) Advances in geosensor networks. Springer, New York

    Google Scholar 

  • O’Rourke J (1988) Computational geometry in C. Cambridge University Press, New York

    MATH  Google Scholar 

  • Santi P (2005) Topology control in wireless ad hoc and sensor networks. ACM Comput Surv 37:164–194

    Article  Google Scholar 

  • Stefanidis A, Nittel S (2004) GeoSensor networks. CRC, Boca Raton

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Software Engineering, The University of Melbourne, Melbourne, VIC, Australia

    Lars Kulik

Authors
  1. Lars Kulik
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Editor information

Editors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Shashi Shekhar

  2. Management Science and Information Systems Department, Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ, USA

    Hui Xiong

  3. Department of Management Sciences, Tippie College of Business, University of Iowa, Iowa City, IA, USA

    Xun Zhou

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© 2017 Springer International Publishing AG

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Kulik, L. (2017). Geosensor Networks, Formal Foundations. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_499

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