A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics
Systems and Control
2014-12-30 v3 Combinatorics
Abstract
Let f_{k}(n) be the maximum number of time steps taken to reach equilibrium by a system of n agents obeying the k-dimensional Hegselmann-Krause bounded confidence dynamics. Previously, it was known that \Omega(n) = f_{1}(n) = O(n^3). Here we show that f_{1}(n) = \Omega(n^2), which matches the best-known lower bound in all dimensions k >= 2.
Keywords
Cite
@article{arxiv.1406.0769,
title = {A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics},
author = {Edvin Wedin and Peter Hegarty},
journal= {arXiv preprint arXiv:1406.0769},
year = {2014}
}
Comments
6 pages, one figure. Arxiv may flag for text overlap with a companion paper which we are uploading simoultaneously, as there is some similar text in the introductions to the two papers. Version 2: Some minor glitches fixed: an error in Footnote 2, some spelling mistakes and an incomplete reference in the bibliography. Version 3: This version accepted for publication