5 papers
Bifunction and Interlevel Delaunay Trifiltrations
Ãngel Javier Alonso, Michael Kerber, Tung Lam +2
A key property of the Delaunay filtration is that it is topologically (i.e., weakly) equivalent to the offset (union-of-balls) filtration. Recently, this filtration has been extend…
(Almost-)Optimal FPT Algorithm and Kernel for -Cycle on Planar Graphs
Harmender Gahlawat, Abhishek Rathod, Meirav Zehavi
Research of cycles through specific vertices is a central topic in graph theory. In this context, we focus on a well-studied computational problem, \textsc{-Cycle}: given an und…
Keeping it sparse: Computing Persistent Homology revisited
Ulrich Bauer, Talha Bin Masood, Barbara Giunti +3
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topo…
Fast Algorithms for Minimum Homology Basis
Amritendu Dhar, Vijay Natarajan, Abhishek Rathod
We study the problem of finding a minimum homology basis, that is, a lightest set of cycles that generates the -dimensional homology classes with coefficients in…
Geometric Localization of Homology Cycles
Amritendu Dhar, Vijay Natarajan, Abhishek Rathod
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is cur…