Near-linear-time algorithm for the geodetic Radon number of grids

作者：Dourado Mitre Costa; Pereira de Sa Vinicius Gusmao; Rautenbach Dieter; Szwarcfiter Jayme Luiz

来源：Discrete Applied Mathematics, 2016, 210: 277-283.

DOI：10.1016/j.dam.2015.05.001

• Graph convexity
• Geodetic convexity
• Radon number
• Grids

The Radon number of a graph is the minimum integer r such that all sets of at least r of its vertices can be partitioned into two subsets whose convex hulls intersect. Determining the Radon number of general graphs in the geodetic convexity is NP-hard. In this paper, we show the problem is polynomial for d-dimensional grids, for all d >= 1. The proposed algorithm runs in near-linear (O (d (log d)(1/2)) time for grids of arbitrary sizes, and in sub-linear O (log d) time when all grid dimensions have the same size.

• 出版日期2016-9-10