Paper Info
Title
Maximizing the number of independent labels in the plane
Abstract
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 Δ) 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 Δ 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 + nΔk-1) time respectively for the fixed-height rectangle label placement model in the plane, we extend our method to improve their algorithms and present a (1 + 1/k)-factor PTAS algorithm that runs in O(n log n + kn log4 Δ + Δk-1) time using O(kΔ3 log4 Δ + kΔk-1) storage.
Year
DOI
Venue
2007
10.1007/978-3-540-73814-5_13
FAW
Keywords
Field
DocType
horizontal line,n log,label number maximization model,fixed-height rectangle label placement,n log n,factor ptas algorithm,maximum number,independent label,position label model,single line,maximum independent set,decision models,dynamic programming algorithm,information processing
Dynamic programming,Combinatorics,GEOM,Rectangle,Time complexity,Map labeling,Horizontal line test,Maximization,Polynomial-time approximation scheme,Mathematics
Conference
Volume
ISSN
ISBN
4613
0302-9743
3-540-73813-4
Citations 
PageRank 
References 
2
0.41
18
Authors
3
Name
Order
Citations
PageRank
Kuen-Lin Yu120.41
Chung-shou Liao232020.95
D.T. Lee362778.14