doc. RNDr. Dušan Knop, Ph.D.

2024 - 2026

The emerging theory of game comonads establishes a fruitful interplay between category theory, mathematical logic, and algorithms. This theory has shown its power when obtaining new Lovasz-type theorems, preservation theorems and decomposition theorems in finite model theory. In our recent work we show that the theory of game comonads can be leveraged to obtain the two traditional Courcelle theorems, stating FPT decidability of monadic second order logic on classes of bounded tree-width and clique-width. This result is only a first step in concrete algorithmic applications of the theory. The abstract setting of game comonads is a good candidate for a systematic treatment of algorithmic problems. The first objective of the project is to formulate a general theory of FPT decidability in terms of game comonads. To start with, we describe some of the important model-theoretic algorithms.

2022

When collecting user data nowadays we care about these being sufficiently anonymous, that is, we usually replace the real data with some perturbed data so that we protect the sole identity of the end-user. This is a challenging task both from computational and algorithmical (theoretic) approach. Therefore we often have to employ advanced methods of analysis and algorithmic techniques to identify tractable cases. We will identify new paramaters that attain low values in realworld data and analyze if these result in fixed-parameter tractable case or to parameterized hardness.

2022 - 2024

Fixed-parameter tractability and approximation algorithms are nowadays standard tools for design of algorithms for hard problems in the area of Computational Social Choice. Surprisingly, kernelization, a prominent technique in FPT algorithmics, is not used as often to tackle social choice problems. Kernelization is a formalism of safe data reduction which we believe does have its place in all research disciplines dealing with large and complex datasets. The most recent approach is the so-called lossy kernelization which on the one hand cooperates with approximation algorithms (unlike kernelization which can only be pipelined with exact algorithms) and on the other hand, allows circumventing hardness results (in exchange for introducing a possible loss in the quality of the solution).

2024 - 2026

V souladu s výzvou projekt umožní mezinárodní mobilitu výzkumným pracovníkům, kterým byl v minulých letech schválen projekt Horizont 2020 z programu Marie Skłodowska-Curie Individual / Postdoctoral Fellowships, jež dosáhl hodnocení alespoň 70 %, ale z důvodů nedostatku financí byl zařazen do kategorie tzv. no-money projektů. Projekt bude realizován pracovními pobyty zahraničních VP na ČVUT. Hlavním cílem projektu je podpora profesního růstu výzkumných pracovníků, kvalitního výzkumu, vzdělávání pro praxi a rozvoje komunikace a spolupráce. Na FIT se jedná o příjezdovou mobilitu na 24 měsíců výzkumného pracovníka, Foivos Fioravantes Ph.D., z Francie. Školitel je doc. Ing. Dušan Knop, Ph.D.

2022 - 2024

Fixed-parameter tractability and approximation algorithms are nowadays standard tools for design of algorithms for hard problems in the area of Computational Social Choice. Surprisingly, kernelization, a prominent technique in FPT algorithmics, is not used as often to tackle social choice problems. Kernelization is a formalism of safe data reduction which we believe does have its place in all research disciplines dealing with large and complex datasets. The most recent approach is the so-called lossy kernelization which on the one hand cooperates with approximation algorithms (unlike kernelization which can only be pipelined with exact algorithms) and on the other hand, allows circumventing hardness results (in exchange for introducing a possible loss in the quality of the solution). This project aims on filling this gap of usage of these tools in computational social choice. The suggested line of research continues our current studies in this area and the new proposed directions will need novel algorithmic approaches as they focus on the boundaries of traceability. We have identified several interesting questions where there is potential to apply the above. Our aim is to significantly deepen our understanding of these computationally hard problems by providing polynomial-sized (lossy) kernels or showing that the problems are resistant to this line of attack.

2022

New Frontiers in Computational Social Choice

2021 - 2022

Výpočetní kolektivní volba (Computational Social Choice) je moderní oblast informatiky, ve které se setkává teoretická informatika a teorie her (ekonomie). Mnoho zásadních problémů v této oblasti je NP-těžkých, proto se začala v poslední dekádě stále častěji uplatňovat tzv. parametrizovaná analýza, která si klade za cíl identifikovat parametry, jejichž zafixování na malých hodnotách vede k efektivní řešitelnosti daného problému. V předkládaném projektu se hodláme zaměřit na strukturální parametry (mezi nejznámější bezpochyby patří stromová šířka) vstupních instancí, čímž omezíme například vzájemnou interakci mezi agenty hledajícími kolektivní rozhodnutí a podobně.