Sigma-local graphs

We introduce and analyze σ-local graphs, based on a definition of locality by Erickson [12]. We present two algorithms to construct such graphs, for any real number σ > 1 and any set S of n points. These algorithms run in time O(σd n + n log n) for sets in Rd and O(n log3 n log log n + k) for sets in the plane, where k is the size of the output. For sets in the plane, algorithms to find the minimum or maximum σ such that the corresponding graph has properties such as connectivity, planarity, and no-isolated vertex are presented, with complexities in O(n logO(1) n). These algorithms can also be used to efficiently construct the corresponding graphs.

• Type: Journal
• Year: 2010
• Where: JDA
• Authors: Prosenjit Bose, Sébastien Collette, Stefan Langerman, Anil Maheshwari, Pat Morin, Michiel H. M. Smid
• Keywords: Algorithms, Corresponding Graphs, JDA 2010, Real Number