Complexity theory is a fundamental branch of theoretical computer science that categorises computational problems according to their inherent difficulty and the resources required to solve them. At ...

Abstract: In this paper, we consider the inverse graph filtering process when the original filter is a polynomial of some graph shift on a simple connected graph. The Chebyshev polynomial ...

Abstract: Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose ...

The field of polynomial systems occupies a central role in computational mathematics, where the intricate interplay between algebra, geometry, and computational complexity is evident. Research in this ...

Overview This project implements algorithms from the paper "Tracking Paths in Polynomial Time", which explores solutions to the Tracking Paths Problem—determining a minimal set of vertices (or edges) ...

We consider the problem of computing optimal policies of finite-state finite-action Markov decision processes (MDPs). A reduction to a continuum of constrained MDPs (CMDPs) is presented such that the ...

This is a collection of algorithms for checking intersectivity of a polynomial. This was developed for my PhD thesis in the pure math department at the University of Waterloo, Ontario, Canada. Some ...

From powering search engines to securing data and optimizing networks, algorithms underpin nearly every aspect of modern technology. Understanding how efficiently they can solve problems — and where ...