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Geometry — Intuitive, Discrete, and Convex pp 219–257Cite as

Survey on Decomposition of Multiple Coverings

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 24))

Abstract

The study of multiple coverings was initiated by Davenport and L. Fejes Tóth more than 50 years ago. In 1980 and 1986, the first named author published the first papers about decomposability of multiple coverings. It was discovered much later that, besides its theoretical interest, this area has practical applications to sensor networks. Now there is a lot of activity in this field with several breakthrough results, although, many basic questions are still unsolved. In this survey, we outline the most important results, methods, and questions.

Research partially supported by Swiss National Science Foundation Grants 200021- 137574 and 200020-144531, by Hungarian Science Foundation Grant OTKA NN 102029 under the EuroGIGA programs ComPoSe and GraDR, and by NSF grant CCF-08-30272.

Supported by János Bolyai Research Scholarship of the Hungarian Academy of Sciences, OTKA PD 104386 and OTKA NN 102029 under EUROGIGA project GraDR 10-EuroGIGA-OP-003. Part of this work was done in Lausanne and supported by Swiss National Science Foundation Grant 200021-125287/1.

Supported by OTKA K 83767 and by OTKA NN 102029 under EUROGIGA project GraDR 10-EuroGIGA-OP-003.

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Author information

Authors and Affiliations

  1. Ecole Polytechnique Fédérale de Lausanne, Switzerland

    János Pach

  2. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    János Pach & Géza Tóth

  3. Department of Mathematics, Eötvös University, Budapest, Hungary

    Dömötör Pálvölgyi

Authors
  1. János Pach
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  2. Dömötör Pálvölgyi
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  3. Géza Tóth
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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

    Imre Bárány , Károly J. Böröczky , Gábor Fejes Tóth  & János Pach , ,  & 

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© 2013 János Bolyai Mathematical Society and Springer-Verlag

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Pach, J., Pálvölgyi, D., Tóth, G. (2013). Survey on Decomposition of Multiple Coverings. In: Bárány, I., Böröczky, K.J., Tóth, G.F., Pach, J. (eds) Geometry — Intuitive, Discrete, and Convex. Bolyai Society Mathematical Studies, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41498-5_9

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