3 citations · 3 across the 6 of their papers we have counts for
11 papers
Bifunction and Interlevel Delaunay Trifiltrations
Ángel 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…
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…
Cup Product Persistence and Its Efficient Computation
Tamal K. Dey, Abhishek Rathod
It is well-known that the cohomology ring has a richer structure than homology groups. However, until recently, the use of cohomology in persistence setting has been limited to spe…
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…
Parameterized inapproximability of Morse matching
Ulrich Bauer, Abhishek Rathod
We study the problem of minimizing the number of critical simplices from the point of view of inapproximability and parameterized complexity. We first show inapproximability of Min…
The complexity of high-dimensional cuts
Ulrich Bauer, Abhishek Rathod, Meirav Zehavi
Cut problems form one of the most fundamental classes of problems in algorithmic graph theory. For instance, the minimum cut, the minimum - cut, the minimum multiway cut, and…
Parametrized Complexity of Expansion Height
Ulrich Bauer, Abhishek Rathod, Jonathan Spreer
Deciding whether two simplicial complexes are homotopy equivalent is a fundamental problem in topology, which is famously undecidable. There exists a combinatorial refinement of th…
Hardness of Approximation for Morse Matching
Ulrich Bauer, Abhishek Rathod
Discrete Morse theory has emerged as a powerful tool for a wide range of problems, including the computation of (persistent) homology. In this context, discrete Morse theory is use…
Approximation Algorithms for Max-Morse Matching
Abhishek Rathod, Talha Bin Masood, Vijay Natarajan
In this paper, we prove that the Max-Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch. We describe two different approximation alg…