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CombiCompGeom

Financiado

Combinatorial Aspects of Computational Geometry

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... ver más

31/08/2022

BGU

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

BENGURION UNIVERSITY OF THE NEGEV No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Ver 2 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2022-08-31

ERC-StG-2015: ERC Starting Grant

I+D

Cerrada hace 9 años

0% 100% 100%

2 Participantes

BGU

1.30M€ | Lider

MAZEL INGENIEROS

771.14K€ | Participante

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Duración del proyecto: 75 meses Fecha Inicio: 2016-05-30
Fecha Fin: 2022-08-31

Líder del proyecto

BENGURION UNIVERSITY OF THE NEGEV No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 1M€

Descripción del proyecto 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.

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