Until recently no algorithm existed for computing the relative neighbourhood graph of n points on the plane in less than O(n2) worst-case time. Urquhart recently presented an O(n log n) algorithm for solving this problem. In this letter it is shown that Urquhart's algorithm does not always work and hence finding an O(n log n) algorithm remains an open problem.
- Graph theory
- Pattern recognition
ASJC Scopus subject areas
- Electrical and Electronic Engineering