What is running time of Voronoi diagram for Manhattan distance l1 norm?

394 Views Asked by At

Cannot find the algorithm for Voronoi on Manhattan distance and its running time. Can someone point to the relevant resources?

Thank you

1

There are 1 best solutions below

0
On

This question has been long over due, but if the OP still wants a reference, then they should consider the following:

  • For general $\ell_p$ norms consider:

Chew, L. Paul; Kedem, Klara; Sharir, Micha; Tagansky, Boaz; Welzl, Emo, Voronoi diagrams of lines in 3-space under polyhedral convex distance functions, Clarkson, K. (ed.), Proceedings of the 6th annual ACM-SIAM symposium on discrete algorithms, San Francisco, CA, USA, January 22-24, 1995. Philadelphia, PA: SIAM. 197-204 (1995). ZBL0848.68107.

  • For $\ell_1$ norm (Manhattan distance) in particular:

Hwang, F. K., An O(n log n) algorithm for rectilinear minimal spanning trees, J. Assoc. Comput. Mach. 26, 177-182 (1979). ZBL0395.68064.

Lee, D. T.; Wong, C. K., Voronoi diagrams in $L_1(L_\infty)$ metrics with 2-dimensional storage applications, SIAM J. Comput. 9, 200-211 (1980). ZBL0447.68111.