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Combinatorial Structures and Processes

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.

Coordinator

UNIVERZITA KARLOVA
Net EU contribution
€ 547 400,00
Address
Ovocny Trh 560/5
116 36 Praha 1
Czechia

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Region
Praha Hlavní město Praha
Activity type
Higher or Secondary Education Establishments
Non-EU contribution
€ 119 600,00

Participants (2)

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Israel
Net EU contribution
€ 92 000,00
Address
Senate Building Technion City
32000 Haifa

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Activity type
Higher or Secondary Education Establishments
Non-EU contribution
€ 0,00
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France
Net EU contribution
€ 110 400,00
Address
Rue Michel Ange 3
75794 Paris

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Region
Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
Non-EU contribution
€ 0,00

Partners (4)

Partner

Partner organisations contribute to the implementation of the action, but do not sign the Grant Agreement.

Simon Fraser University
Canada
Net EU contribution
€ 0,00
Address
University Drive 8888
V5A 1S6 Burnaby

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Activity type
Higher or Secondary Education Establishments
Non-EU contribution
€ 9 200,00
Partner

Partner organisations contribute to the implementation of the action, but do not sign the Grant Agreement.

Los Alamos National Security LLC
United States
Net EU contribution
€ 0,00
Address
Ms 187
87545 Los Alamos Nm

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Activity type
Private for-profit entities (excluding Higher or Secondary Education Establishments)
Non-EU contribution
€ 0,00
Partner

Partner organisations contribute to the implementation of the action, but do not sign the Grant Agreement.

TRUSTEES OF PRINCETON UNIVERSITY
United States
Net EU contribution
€ 0,00
Address
Nassau Hall 1
08544-2001 Princeton, Nj

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Activity type
Higher or Secondary Education Establishments
Non-EU contribution
€ 4 600,00
Partner

Partner organisations contribute to the implementation of the action, but do not sign the Grant Agreement.

RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY
United States
Net EU contribution
€ 0,00
Address
Rutgers Plaza 3
08901 New Brunswick

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Activity type
Higher or Secondary Education Establishments
Non-EU contribution
€ 105 800,00