Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles

Given a point set P in the plane, the Delaunay graph with respect to axis-parallel rectangles is a graph defined on the vertex set P, whose two points p, q P are connected by an edge if and only if there is a rectangle parallel to the coordinate axes that contains p and q, but no other elements of P. The following question of Even et al. [ELRS03] was motivated by a frequency assignment problem in cellular telephone networks. Does there exist a constant c > 0 such that the Delaunay graph of any set of n points in general position in the plane contains an independent set of size at least cn? We answer this question in the negative, by proving that the largest independent set in a randomly and uniformly selected point set in the unit square is O(n log2

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Xiaomin Chen, János Pach, Mario Szegedy, Gábor Tardos
• Keywords: Algorithms, Delaunay Graph, Independent Set, SODA 2008, Vertex Set P