CORDIS
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CORDIS

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Combinatorial Structures and Processes

Project information

Grant agreement ID: 823748

Status

Ongoing project

  • Start date

    1 January 2019

  • End date

    31 December 2022

Funded under:

H2020-EU.1.3.3.

  • Overall budget:

    € 869 400

  • EU contribution

    € 749 800

Coordinated by:

UNIVERZITA KARLOVA

Czechia

Objective

The project brings together combinatorialists of various fields with the aim that they will enrich each other’s techniques. The tool kits they will bring include topology, probability, statistical physics and algebra. These should apply to matching problems (a central topic in combinatorics), algorithmic problems, coloring problems (which are decompositions into independent sets or matchings) and homomorphisms (a generalization of colorings).
One umbrella under which many of these can be gathered is the intersection of two matroids, a notion generalizing that of matchings in bipartite graphs. Researchers are baffled by a strange phenomenon – that moving from one matroid to the intersection of two matroids sometimes costs little. The algorithmic problems are indeed harder, but the difference between min and max in the min-max theorems suffer only a conjectured penalty of 1.
This connects with a second direction of the research, fine grained complexity, which deals with polynomially solvable problems, and aims to prove, under widely believed assumptions, lower bounds on the exponents in the polynomial bounds. A major question in the field is proving similar tight bounds for approximation problems.
A direction connecting matchings, colorings and homomorphisms was initiated recently in statistical physics. It investigates typical algorithmic complexity, of computational problems taken under some probability distribution. While the worst case complexity questions are difficult in general and not clearly practically relevant, when we restrict to a given probability distribution of instances and when we are interested in high probability results, progress has been made, that has contributed also algorithmic insights beyond the probabilistic setting. We propose to address several outstanding open questions from the field.
Finally we will work on a deep connection, studied by some of the researchers in the project, between Ramsey theory, Model theory and graph homomorphisms.
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Coordinator

UNIVERZITA KARLOVA

Address

Ovocny Trh 560/5
116 36 Praha 1

Czechia

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 529 000

Participants (2)

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY

Israel

EU Contribution

€ 110 400

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

France

EU Contribution

€ 110 400

Partners (4)

Simon Fraser University

Canada

Los Alamos National Security LLC

United States

TRUSTEES OF PRINCETON UNIVERSITY

United States

RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY

United States

Project information

Grant agreement ID: 823748

Status

Ongoing project

  • Start date

    1 January 2019

  • End date

    31 December 2022

Funded under:

H2020-EU.1.3.3.

  • Overall budget:

    € 869 400

  • EU contribution

    € 749 800

Coordinated by:

UNIVERZITA KARLOVA

Czechia