Maximizing the Number of Independent Labels in the Plane

In this paper, we consider a map labeling problem to maximize the number of independent labels in the plane. We first investigate the point labeling model that each label can be placed on a given set of anchors on a horizontal line. It is known that most of the map labeling decision models on a single line (horizontal or slope line) can be easily solved. However, the label number maximization models are more difficult (like 2SAT vs. MAX-2SAT). We present an O(n log ∆) time algorithm for the four position label model on a horizontal line based on dynamic programming and a particular analysis, where n is the number of the anchors and ∆ is the maximum number of labels whose intersection is nonempty. As a contrast to Agarwal et al.’s result [Comput. Geom. Theory Appl. 11 (1998) 209-218] and Chan’s result [Inform. Process. Letters 89(2004) 19-23] in which they provide (1 + 1/k)-factor PTAS algorithms that run in O(n log n + n2k−1 ) time and O(n log n + n∆k−1 ) time respectiv...

• Type: Conference
• Year: 2007
• Where: FAW
• Authors: Kuen-Lin Yu, Chung-Shou Liao, Der-Tsai Lee
• Keywords: 1/k)-factor Ptas Algorithm, FAW 2007, Horizontal Line, Label