Abstract
Purchase PDF (574 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (8)
Purchase PDF (593 K)
doi:10.1016/S0020-0190(98)00190-2 
Copyright © 1999 Published by Elsevier Science B.V.
Labeling a rectilinear map more efficiently*1
Received 19 August 1998.
References and further reading may be available for this article. To view references and further reading you must purchase this article.
Abstract
Given a rectilinear map consisting of n disjoint line segments, the corresponding labeling problem is to place a rectangle at each segment, allowing three possible positions, such that the rectangles do not intersect. This problem has a decision and a height maximization version. This paper improves results from Poon, Zhu and Chin's “A polynomial time solution for labeling a rectilinear map” (Inform. Process. Lett. 65 (1998) 201–207). An algorithm is proposed that improves the running time of the decision problem from O(n2) to O(n log n α (n)), with α(n) the inverse of the Ackermann function. An algorithm for the height maximization problem is presented that lowers the running time from O(n2 log n) to O(n log2 n α (n)). These bounds are for the pointer machine model; in the RAM model we can drop the α(n) factor. We also describe an algorithm to solve the decision labeling problem where segments of arbitrary directions are allowed in O(n4/3polylog n) time and space.
Author Keywords: Computational geometry; Map labeling
