Descripción del proyecto
Impulsar la investigación en teoría de grafos
La teoría de grafos se ocupa del estudio de los grafos, que son fundamentales para modelar las relaciones de pareja entre los objetos. Los grafos pueden utilizarse para modelar muchos tipos de relaciones en sistemas físicos, biológicos, sociales y de información. Financiado por las Acciones Marie Skłodowska-Curie, en el proyecto CoSP se fusionarán los conocimientos de las matemáticas discretas con la informática teórica para estudiar una serie de temas interesantes de la teoría de grafos. Entre ellos se encuentran la teoría de emparejamiento de grafos e hipergrafos, los algoritmos complejos, los problemas de coloración y los homomorfismos de grafos.
Objetivo
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.
Ámbito científico
- natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logic
- natural sciencesmathematicspure mathematicstopology
- natural sciencesmathematicspure mathematicsalgebra
- natural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theory
- natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics
Palabras clave
Programa(s)
Régimen de financiación
MSCA-RISE - Marie Skłodowska-Curie Research and Innovation Staff Exchange (RISE)Coordinador
116 36 Praha 1
Chequia