5 papers
Tracking the Persistence of Harmonic Chains: Barcode and Stability
Tao Hou, Salman Parsa, Bei Wang
The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks t…
Harmonic Chain Barcode and Stability
Salman Parsa, Bei Wang
The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of the space of data, a persistence barco…
On the Parameterized Complexity of Motion Planning for Rectangular Robots
Iyad Kanj, Salman Parsa
We study computationally-hard fundamental motion planning problems where the goal is to translate axis-aligned rectangular robots from their initial positions to their final po…
Revisiting Graph Persistence for Updates and Efficiency
Tamal K. Dey, Tao Hou, Salman Parsa
It is well known that ordinary persistence on graphs can be computed more efficiently than the general persistence. Recently, it has been shown that zigzag persistence on graphs al…
On links of vertices in simplicial -complexes embeddable in the euclidean -space
Salman Parsa
We consider -dimensional simplicial complexes which can be PL embedded in the -dimensional euclidean space. In short, we show that in any such complex, for any three vertice…