Projektbeschreibung
Antrieb für die Forschung zur Graphentheorie
Die Graphentheorie beschäftigt sich mit Graphen, welche ein Grundbaustein für die Modellierung der paarweisen Beziehungen zwischen Objekten sind. Graphen können für die Modellierung verschiedenster Beziehungen in physikalischen, biologischen, sozialen und Informationssystemen eingesetzt werden. Finanziert über die Marie-Skłodowska-Curie-Maßnahmen wird das Projekt CoSP das Fachwissen der diskreten Mathematik mit theoretischer Computerwissenschaft kombinieren, um mehrere interessante Punkte der Graphentheorie zu erforschen. Dazu gehört die Theorie zu Matchings von Graphen und Hypergraphen, komplexe Algorithmen, Färbungsprobleme und Homomorphismen.
Ziel
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.
Wissenschaftliches Gebiet
- natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logic
- natural sciencesmathematicspure mathematicstopology
- natural sciencesmathematicspure mathematicsalgebra
- natural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theory
- natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics
Schlüsselbegriffe
Programm/Programme
Aufforderung zur Vorschlagseinreichung
Andere Projekte für diesen Aufruf anzeigenKoordinator
116 36 Praha 1
Tschechien