21 citations · 217 across the 52 of their papers we have counts for
69 papers
Computing Conley-Morse Persistence Barcode Efficiently by Updating Matrix Decompositions
Tamal K. Dey, Andrew Haas, Michał Lipiński
Recent advances in combinatorial dynamical systems that generalize the classic discrete Morse theory have prompted algorithmic studies of combinatorial vector fields. In this regar…
Linked Barcode for Persistence Induced by Filtrations
Tamal K. Dey, Gilberto Gonzalez-Arroyo, Tao Hou
The well-known persistence algorithm summarizes the evolution of homological cycles into what is called a \emph{barcode} while scanning an input simplicial filtration. We show that…
Updating zigzag representatives efficiently
Tamal K. Dey, Tao Hou, Dmitriy Morozov
Computation of zigzag persistence has progressed in recent years, with results showing that complexities of many problems closely align with those in the non-zigzag setting. The ma…
Limit Computation Over Posets via Minimal Initial Functors
Tamal K. Dey, Michael Lesnick
It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic impl…
Fast free resolutions of bifiltered chain complexes
Ulrich Bauer, Tamal K. Dey, Michael Kerber +2
In a -critical bifiltration, every simplex enters along a staircase with at most steps. Examples with include degree-Rips bifiltrations and models of the multicover bi…
Computing Projective Implicit Representations from Poset Towers
Tamal K. Dey, Florian Russold
A family of simplicial complexes connected by simplicial maps and indexed by a finite poset is called a poset tower. Poset towers subsume multi-parameter filtrations, zigzag fi…