5 citations · 9 across the 7 of their papers we have counts for
8 papers
Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry
Surya Majumder, Daniel Widdowson, Yury Elkin +4
Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units.…
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…
A new compressed cover tree for k-nearest neighbour search and the stable-under-noise mergegram of a point cloud
Yury Elkin
This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and a…
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…
Isometry invariant shape recognition of projectively perturbed point clouds by the mergegram extending 0D persistence
Yury Elkin, Vitaliy Kurlin
Rigid shapes should be naturally compared up to rigid motion or isometry, which preserves all inter-point distances. The same rigid shape can be often represented by noisy point cl…
A new near-linear time algorithm for k-nearest neighbor search using a compressed cover tree
Yury Elkin, Vitaliy Kurlin
Given a reference set of points and a query set of points in a metric space, this paper studies an important problem of finding -nearest neighbors of every point…
The mergegram of a dendrogram and its stability
Yury Elkin, Vitaliy Kurlin
This paper extends the key concept of persistence within Topological Data Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in unorganized data such as cl…
A fast approximate skeleton with guarantees for any cloud of points in a Euclidean space
Yury Elkin, Di Liu, Vitaliy Kurlin
The tree reconstruction problem is to find an embedded straight-line tree that approximates a given cloud of unorganized points in up to a certain error. A practical…