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of 33
pro vyhledávání: '"Rathod, Abhishek"'
Autor:
Tabib, Wennie, Stecklein, John, McDowell, Caleb, Goel, Kshitij, Jonathan, Felix, Rathod, Abhishek, Kokoski, Meghan, Burkholder, Edsel, Wallace, Brian, Navarro-Serment, Luis Ernesto, Bakshi, Nikhil Angad, Gupta, Tejus, Papernick, Norman, Guttendorf, David, Kahn, Erik E., Kasemer, Jessica, Holdaway, Jesse, Schneider, Jeff
Rapid search and rescue is critical to maximizing survival rates following natural disasters. However, these efforts are challenged by the need to search large disaster zones, lack of reliability in the communications infrastructure, and a priori unk
Externí odkaz:
http://arxiv.org/abs/2410.08507
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 currently no known optimality criterion that localizes classes geometrica
Externí odkaz:
http://arxiv.org/abs/2406.03183
Autor:
Dey, Tamal K., Rathod, Abhishek
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 speeding up of barcode computations. Some of the recently introduced inva
Externí odkaz:
http://arxiv.org/abs/2212.01633
Autor:
Bauer, Ulrich, Masood, Talha Bin, Giunti, Barbara, Houry, Guillaume, Kerber, Michael, Rathod, Abhishek
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 topological data analysis where matrix reduction is the major subroutine t
Externí odkaz:
http://arxiv.org/abs/2211.09075
Publikováno v:
IEEE Transactions on Robotics 2023
Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continu
Externí odkaz:
http://arxiv.org/abs/2210.12583
We study the problem of finding a minimum homology basis, that is, a lightest set of cycles that generates the $1$-dimensional homology classes with $\mathbb{Z}_2$ coefficients in a given simplicial complex $K$. This problem has been extensively stud
Externí odkaz:
http://arxiv.org/abs/2109.04567
Autor:
Bauer, Ulrich, Rathod, Abhishek
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-Morse Matching within a factor of $2^{\log^{(1-\epsilon)}n}$. Our sec
Externí odkaz:
http://arxiv.org/abs/2109.04529
Cut problems form one of the most fundamental classes of problems in algorithmic graph theory. For instance, the minimum cut, the minimum $s$-$t$ cut, the minimum multiway cut, and the minimum $k$-way cut are some of the commonly encountered cut prob
Externí odkaz:
http://arxiv.org/abs/2108.10195
Publikováno v:
27th Annual European Symposium on Algorithms (ESA 2019), Leibniz International Proceedings in Informatics (LIPIcs) vol. 144, 2019, p. 13:1-15
Deciding whether two simplicial complexes are homotopy equivalent is a fundamental problem in topology, which is famously undecidable. There exists a combinatorial refinement of this concept, called simple-homotopy equivalence: two simplicial complex
Externí odkaz:
http://arxiv.org/abs/1910.09228
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