11 citations · 54 across the 16 of their papers we have counts for
6 papers · 1 filter
Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006
Yury Elkin, Vitaliy Kurlin
This paper is motivated by the k-nearest neighbors search: given an arbitrary metric space, and its finite subsets (a reference set R and a query set Q), design a fast algorithm to…
Densest plane group packings of regular polygons
Miloslav Torda, John Y. Goulermas, Vitaliy Kurlin +1
Packings of regular convex polygons (-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discr…
Density functions of periodic sequences
Olga Anosova, Vitaliy Kurlin
Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-poin…
Recognition of near-duplicate periodic patterns by continuous metrics with approximation guarantees
Olga Anosova, Daniel Widdowson, Vitaliy Kurlin
This paper rigorously solves the challenging problem of recognizing periodic patterns under rigid motion in Euclidean geometry. The 3-dimensional case is practically important for…
Entropic trust region for densest crystallographic symmetry group packings
Miloslav Torda, John Y. Goulermas, Roland Púček +1
Molecular crystal structure prediction (CSP) seeks the most stable periodic structure given the chemical composition of a molecule and pressure-temperature conditions. Modern CSP s…
Paired compressed cover trees guarantee a near linear parametrized complexity for all -nearest neighbors search in an arbitrary metric space
Yury Elkin, Vitaliy Kurlin
This paper studies the important problem of finding all -nearest neighbors to points of a query set in another reference set within any metric space. Our previous work d…