2 citations · 3 across the 8 of their papers we have counts for
6 papers · 1 filter
Distributed Computation of Persistent Cohomology
Arnur Nigmetov, Dmitriy Morozov
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable f…
Fast Merge Tree Computation via SYCL
Arnur Nigmetov, Dmitriy Morozov
A merge tree is a topological descriptor of a real-valued function. Merge trees are used in visualization and topological data analysis, either directly or as a means to another en…
Topological Optimization with Big Steps
Arnur Nigmetov, Dmitriy Morozov
Using persistent homology to guide optimization has emerged as a novel application of topological data analysis. Existing methods treat persistence calculation as a black box and b…
Efficient Approximation of the Matching Distance for 2-parameter persistence
Michael Kerber, Arnur Nigmetov
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matchi…
Metric Spaces with Expensive Distances
Michael Kerber, Arnur Nigmetov
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in te…
Geometry Helps to Compare Persistence Diagrams
Michael Kerber, Dmitriy Morozov, Arnur Nigmetov
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geomet…