Description du projet
Stimuler la recherche en théorie des graphes
La théorie des graphes traite l’étude de graphes qui sont essentiels pour modéliser des relations par paires d’objets. Les graphes peuvent servir à modéliser de nombreux types de relations dans des systèmes physiques, biologiques, sociaux et informatiques. Le projet CoSP, financé par le programme Actions Marie Skłodowska-Curie, combinera l’expertise en mathématiques discrètes et en informatique théorique pour étudier un certain nombre de sujets intéressants dans la théorie des graphes. Ceux-ci comprennent la théorie analogue des graphes et des hypergraphes, les algorithmes complexes, les problèmes de coloration et les homomorphismes de graphes.
Objectif
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.
Champ scientifique
- natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logic
- natural sciencesmathematicspure mathematicstopology
- natural sciencesmathematicspure mathematicsalgebra
- natural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theory
- natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics
Mots‑clés
Programme(s)
Régime de financement
MSCA-RISE - Marie Skłodowska-Curie Research and Innovation Staff Exchange (RISE)Coordinateur
116 36 Praha 1
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