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Rigid and Globally Rigid Graphs with Pinned Vertices

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Fete of Combinatorics and Computer Science

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 20))

Abstract

We consider rigid and globally rigid bar-and-joint frameworks (resp. graphs) in which some joints (resp. vertices) are pinned down and hence their positions are fixed. We give an overview of some old and new results of this branch of combinatorial rigidity with an emphasis on the related optimization problems.

In one of these problems the goal is to find a set P of vertices of minimum total cost for which the positions of all vertices become uniquely determined when P is pinned down. For this problem, which is motivated by the localization problem in wireless sensor networks, we give a constant factor approximation algorithm.

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Author information

Authors and Affiliations

  1. Department of Operations Research, Eötvös University, Pázmány Péter sétány 1/C, 1117 Budapest, Hungary

    Tibor Jordán

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  1. Tibor Jordán
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Editor information

Editors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Gyula O. H. Katona

  2. Centre for Mathematics and Computer Science, Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Alexander Schrijver

  3. Department of Computer Science, Eötvös University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary

    Tamás Szőnyi

  4. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Gábor Sági

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© 2010 János Bolyai Mathematical Society and Springer-Verlag

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Jordán, T. (2010). Rigid and Globally Rigid Graphs with Pinned Vertices. In: Katona, G.O.H., Schrijver, A., Szőnyi, T., Sági, G. (eds) Fete of Combinatorics and Computer Science. Bolyai Society Mathematical Studies, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13580-4_7

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