31 citations · 52 across the 6 of their papers we have counts for
9 papers
Solving equations and optimization problems with uncertainty
Peter Franek, Marek Krčál, Hubert Wagner
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experi…
On Computability and Triviality of Well Groups
Peter Franek, Marek Krcal
The concept of well group in a special but important case captures homological properties of the zero set of a continuous map on a compact space K that are invariant w…
Robust Satisfiability of Systems of Equations
Peter Franek, Marek Krcal
We study the problem of \emph{robust satisfiability} of systems of nonlinear equations, namely, whether for a given continuous function on a~finite simplicia…
On the Geometric Ramsey Number of Outerplanar Graphs
Josef Cibulka, Pu Gao, Marek Krčál +2
We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey num…
Algorithmic solvability of the lifting-extension problem
Martin Čadek, Marek Krčál, Lukáš Vokřínek
Let and be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group . Assuming that is -connected…
Extendability of continuous maps is undecidable
Martin Cadek, Marek Krcal, Jiri Matousek +2
We consider two basic problems of algebraic topology, the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational…
Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension
Martin Cadek, Marek Krcal, Jiri Matousek +2
For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k>1, there is a polynomia…
Polynomial-time homology for simplicial Eilenberg-MacLane spaces
Marek Krcal, Jiri Matousek, Francis Sergeraert
In an earlier paper of Cadek, Vokrinek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all…
Computing all maps into a sphere
Martin Čadek, Marek Krčál, Jiří Matoušek +3
Given topological spaces X and Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X -> Y . We consider a computational version, wh…