Opis projektu
Wspieranie badań w zakresie teorii grafów
Teoria grafów zajmuje się badaniem grafów, które są podstawą do modelowania relacji między parami obiektów. Grafy mogą służyć do modelowania wielu rodzajów relacji w systemach fizycznych, biologicznych, społecznych i informacyjnych. Finansowany ze środków programu działań „Maria Skłodowska-Curie” projekt CoSP połączy wiedzę z zakresu matematyki dyskretnej z informatyką teoretyczną w celu zbadania szeregu interesujących zagadnień z dziedziny teorii grafów. Należą do nich teoria dopasowania dla grafów i hipergrafów, algorytmy złożone, problemy kolorowania i homomorfizmy grafów.
Cel
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.
Dziedzina nauki
- natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logic
- natural sciencesmathematicspure mathematicstopology
- natural sciencesmathematicspure mathematicsalgebra
- natural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theory
- natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics
Słowa kluczowe
Program(-y)
Zaproszenie do składania wniosków
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