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CombiCompGeom SIGNED

Combinatorial Aspects of Computational Geometry

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EC-Contrib. €

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Project "CombiCompGeom" data sheet

The following table provides information about the project.

Coordinator
BEN-GURION UNIVERSITY OF THE NEGEV 

Organization address
address: .
city: BEER SHEVA
postcode: 84105
website: www.bgu.ac.il

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Total cost 1˙303˙750 €
 EC max contribution 1˙303˙750 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-09-01   to  2021-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    BEN-GURION UNIVERSITY OF THE NEGEV IL (BEER SHEVA) coordinator 1˙303˙750.00

Map

 Project objective

The project focuses on the interface between computational and combinatorial geometry. Geometric problems emerge in a variety of computational fields that interact with the physical world. The performance of geometric algorithms is determined by the description complexity of their underlying combinatorial structures. Hence, most theoretical challenges faced by computational geometry are of a distinctly combinatorial nature.

In the past two decades, computational geometry has been revolutionized by the powerful combination of random sampling techniques with the abstract machinery of geometric arrangements. These insights were used, in turn, to establish state-of-the-art results in combinatorial geometry. Nevertheless, a number of fundamental problems remained open and resisted numerous attempts to solve them.

Motivated by the recent breakthrough results, in which the PI played a central role, we propose two exciting lines of study with the potential to change the landscape of this field.

The first research direction concerns the complexity of Voronoi diagrams -- arguably the most common structures in computational geometry.

The second direction concerns combinatorial and algorithmic aspects of geometric intersection structures, including some fundamental open problems in geometric transversal theory. Many of these questions are motivated by geometric variants of general covering and packing problems, and all efficient approximation schemes for them must rely on the intrinsic properties of geometric graphs and hypergraphs.

Any progress in responding to these challenges will constitute a major breakthrough in both computational and combinatorial geometry.

 Publications

year authors and title journal last update
List of publications.
2018 Kolja Knauer, Leonardo Martínez-Sandoval, Jorge Luis Ramírez Alfonsín
On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial
published pages: 698-719, ISSN: 0179-5376, DOI: 10.1007/s00454-018-9965-4
Discrete & Computational Geometry 60/3 2019-06-06
2018 J. Chappelon, L. Martínez-Sandoval, L. Montejano, L. P. Montejano, J. L. Ramírez Alfonsín
Codimension Two and Three Kneser Transversals
published pages: 1351-1363, ISSN: 0895-4801, DOI: 10.1137/16M1101854
SIAM Journal on Discrete Mathematics 32/2 2019-06-06
2019 Martin Balko
Ramsey numbers and monotone colorings
published pages: 34-58, ISSN: 0097-3165, DOI: 10.1016/j.jcta.2018.11.013
Journal of Combinatorial Theory, Series A 163 2019-06-06
2019 J\'anos Pach, Natan Rubin, and G\'abor Tardos
Planar Point Sets Determine Many Pairwise Crossing Segments
published pages: , ISSN: , DOI:
51st ACM Symposium on Theory of Computing 2019-06-06
2018 János Pach, Natan Rubin, Gábor Tardos
A Crossing Lemma for Jordan curves
published pages: 908-940, ISSN: 0001-8708, DOI: 10.1016/j.aim.2018.03.015
Advances in Mathematics 331 2019-06-06
2018 Martínez-Sandoval, Leonardo; Roldán-Pensado, Edgardo; Rubin, Natan
Further Consequences of the Colorful Helly Hypothesis
published pages: , ISSN: , DOI: 10.4230/lipics.socg.2018.59
International Symposium on Computational Geometry (SoCG 2018) 2019-06-06

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The information about "COMBICOMPGEOM" are provided by the European Opendata Portal: CORDIS opendata.

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