Geometry Methods in Sensor Networks

Alexander Kröller, Technische Universitaet Braunschweig


Nov 23, 2015 from 10:00 AM to 11:00 AM (Europe/Madrid / UTC100)


10 to 12, Room S215, Omega building, Campus Nord, UPC

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The course is open to any interested person. Please confirm to mcomputing at your interest.
For Master in Computing students, this is a 1ECTS course.


A wireless sensor network can be seen - or simplified - as a geometric graph, that is, a
directed or undirected graph with an embedding of the nodes into R2 or R3, where the
presence of edges is controlled by a boolean function. A substantial amount of WSN
research assumes this embedding is known to the nodes, or attempts to reconstruct it. The
latter de nes a class of problems, collectively known as Localization.

The aim of this course is to see how we can exploit the geometry of a WSN without
having to solve the localization problem.
We begin by reviewing why localization is a notoriously hard problem [1, 2, 3, 4], and
why we should therefore seek algorithms that do not need the actual embedding of the
nodes. In the following, we will concentrate on algorithms that use methods from Com-
putational Geometry to establish topological knowledge in the network, without requiring
localization. We will see how to identify the boundary of the WSN [6, 7, 8] and how to
construct topologically meaningful segmentations [6, 9]. We will also see how to use such
structures in applications, for example routing [5].


[1] J. Aspnes, D. K. Goldenberg, and Y.R. Yang. On the computational complexity of sensor network
localization. In Proc. ALGOSENSORS'04, pages 32-44, 2004.
[2] A. Basu, J. Gao, J.S.B. Mitchell, and G. Sabhnani. Distributed localization using noisy distance and
angle information. In Proc. MobiHoc'06, pages 262{273. ACM Press, 2006.
[3] H. Breu and D. G. Kirkpatrick. Unit disk graph recognition is NP-hard. Computational Geometry:
Theory and Applications, 9(1-2):3-24, 1998.
[4] J. Bruck, J. Gao, and A. Jiang. Localization and routing in sensor networks by local angle information.
In Proc. MobiHoc'05, pages 181{192. ACM Press, 2005.
[5] J. Bruck, J. Gao, and A. Jiang. MAP: Medial axis based geometric routing in sensor networks. In
Proc. MobiCom'05. ACM Press, 2005.
[6] A. Kröller, S.P. Fekete, D. P sterer, and S. Fischer. Deterministic boundary recognition and topology
extraction for large sensor networks. In Proc. SODA'06, pages 1000-1009, 2006.
[7] O. Saukh, R. Sauter, M. Gauger, P.J. Marr on, and K. Rothermel. On boundary recognition without
location information in wireless sensor networks. In Proc. IPSN'08, pages 207-218, 2008.
[8] Y.Wang, J. Gao, and J.S.B. Mitchell. Boundary recognition in sensor networks by topological methods.
In Proc. MobiCom'06, pages 122-133. ACM Press, 2006.
[9] X. Zhu, R. Sarkar, and J. Gao. Shape segmentation and applications in sensor networks. In Proc.
INFOCOM'07, pages 1838-1846, 2007.

Supported by the MICINN program "ayudas de movilidad de profesores en másters oficiales" 2008-2009.