Rederiving the Upper Bound for Halving Edges using Cardano's Formula
Computational Geometry
2018-02-13 v1
Abstract
In this paper we rederive an old upper bound on the number of halving edges present in the halving graph of an arbitrary set of points in 2-dimensions which are placed in general position. We provide a different analysis of an identity discovered by Andrejak et al, to rederive this upper bound of . In the original paper of Andrejak et al. the proof is based on a naive analysis whereas in this paper we obtain the same upper bound by tightening the analysis thereby opening a new door to derive these upper bounds using the identity. Our analysis is based on a result of Cardano for finding the roots of a cubic equation. We believe that our technique has the potential to derive improved bounds on the number of halving edges.
Cite
@article{arxiv.1802.03730,
title = {Rederiving the Upper Bound for Halving Edges using Cardano's Formula},
author = {Pintu Chauhan and Manjish Pal and Napendra Solanki},
journal= {arXiv preprint arXiv:1802.03730},
year = {2018}
}