Cel In this proposal we plan to extend mathematical foundations of algorithms for various variants of the minimum cut problem within theoretical computer science.Recent advances in understanding the structure of small cuts and tractability of cut problems resulted in a mature algorithmic toolbox for undirected graphs under the paradigm of parameterized complexity. In this position, we now aim at a full understanding of the tractability of cut problems in the more challenging case of directed graphs, and see opportunities to apply the aforementioned successful structural approach to advance on major open problems in other paradigms in theoretical computer science.The specific goals of the project are grouped in the following three themes.Directed graphs. Chart the parameterized complexity of graph separation problems in directed graphs and provide a fixed-parameter tractability toolbox, equally deep as the one in undirected graphs. Provide tractability foundations for routing problems in directed graphs, such as the disjoint paths problem with symmetric demands.Planar graphs. Resolve main open problems with respect to network design and graph separation problems in planar graphs under the following three paradigms: parameterized complexity, approximation schemes, and cut/flow/distance sparsifiers. Recently discovered connections uncover significant potential in synergy between these three algorithmic approaches.Tree decompositions. Show improved tractability of graph isomorphism testing in sparse graph classes. Combine the algorithmic toolbox of parameterized complexity with the theory of minimal triangulations to advance our knowledge in structural graph theory, both pure (focused on the Erdos-Hajnal conjecture) and algorithmic (focused on the tractability of Maximum Independent Set and 3-Coloring). Dziedzina nauki natural sciencescomputer and information sciencescomputational sciencenatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theory Słowa kluczowe theoretical computer science fixed parameter tractability parameterized complexity structural graph theory cut and flows in graphs directed graphs planar graphs graph decompositions Program(-y) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Temat(-y) ERC-2016-STG - ERC Starting Grant Zaproszenie do składania wniosków ERC-2016-STG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-STG - Starting Grant Instytucja przyjmująca UNIWERSYTET WARSZAWSKI Wkład UE netto € 1 228 250,00 Adres KRAKOWSKIE PRZEDMIESCIE 26/28 00-927 WARSZAWA Polska Zobacz na mapie Region Makroregion województwo mazowieckie Warszawski stołeczny Miasto Warszawa Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 1 228 250,00 Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE netto Rozwiń wszystko Zwiń wszystko UNIWERSYTET WARSZAWSKI Polska Wkład UE netto € 1 228 250,00 Adres KRAKOWSKIE PRZEDMIESCIE 26/28 00-927 WARSZAWA Zobacz na mapie Region Makroregion województwo mazowieckie Warszawski stołeczny Miasto Warszawa Rodzaj działalności Higher or Secondary Education Establishments Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Uczestnictwo w unijnych programach w zakresie badań i innowacji Opens in new window sieć współpracy HORIZON Opens in new window Koszt całkowity € 1 228 250,00
