A combinatorial theorem on labeling squares with points and its application

In this paper, we present a combinatorial theorem on labeling disjoint axis-parallel squares of edge length two using points. Given an arbitrary set of disjoint axis-parallel squares of edge length two, we show that if we label points on the boundary of all squares (one for each square) and define a distance label graph such that there is an edge between any two labeling points if and only if their L-distance is at most 1 - (0 < < 1), then the maximum connected component of the graph contains (1/ ) vertices, which is tight. With this theorem we present a new and simple factor-(3 + ) approximation for labeling points with axis-parallel squares under the slider model. Keywords Square packing . Combinatorics . Map labeling

• Type: Journal
• Year: 2006
• Where: JCO
• Authors: Binhai Zhu, Minghui Jiang
• Keywords: Disjoint Axis-parallel Squares, Distance Label Graph, Edge Length, JCO 2006