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Incidences

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Graph Theory, Combinatorics and Algorithms

Part of the book series: Operations Research/Computer Science Interfaces Series ((volume 34))

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Abstract

We survey recent progress related to the following general problem in combinatorial geometry: What is the maximum number of incidences between m points and n members taken from a fixed family of curves or surfaces in d-space? Results of this kind have found numerous applications to geometric problems related to the distribution of distances among points, to questions in additive number theory, in analysis, and in computational geometry.

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Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    János Pach & Micha Sharir

  2. School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Micha Sharir

Authors
  1. János Pach
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  2. Micha Sharir
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Editor information

Editors and Affiliations

  1. University of Haifa, Israel

    Martin Charles Golumbic  & Irith Ben-Arroyo Hartman  & 

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Pach, J., Sharir, M. (2005). Incidences. In: Golumbic, M.C., Hartman, I.BA. (eds) Graph Theory, Combinatorics and Algorithms. Operations Research/Computer Science Interfaces Series, vol 34. Springer, Boston, MA. https://doi.org/10.1007/0-387-25036-0_11

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