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Full-Text Articles in Discrete Mathematics and Combinatorics
On Communication For Distributed Babai Point Computation, Maiara F. Bollauf, Vinay A. Vaishampayan, Sueli I.R. Costa
On Communication For Distributed Babai Point Computation, Maiara F. Bollauf, Vinay A. Vaishampayan, Sueli I.R. Costa
Publications and Research
We present a communication-efficient distributed protocol for computing the Babai point, an approximate nearest point for a random vector X∈Rn in a given lattice. We show that the protocol is optimal in the sense that it minimizes the sum rate when the components of X are mutually independent. We then investigate the error probability, i.e. the probability that the Babai point does not coincide with the nearest lattice point, motivated by the fact that for some cases, a distributed algorithm for finding the Babai point is sufficient for finding the nearest lattice point itself. Two different probability models for X …
The History Of Algorithmic Complexity, Audrey A. Nasar
The History Of Algorithmic Complexity, Audrey A. Nasar
Publications and Research
This paper provides a historical account of the development of algorithmic complexity in a form that is suitable to instructors of mathematics at the high school or undergraduate level. The study of algorithmic complexity, despite being deeply rooted in mathematics, is usually restricted to the computer science curriculum. By providing a historical account of algorithmic complexity through a mathematical lens, this paper aims to equip mathematics educators with the necessary background and framework for incorporating the analysis of algorithmic complexity into mathematics courses as early on as algebra or pre-calculus.