Geometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider the following generalized geometric spanner problem under L 1 distance: Given a set of disjoint objects S, find a spanning network G with minimum size so that for any pair of points in different objects of S, there exists a path in G with length no more than t times their L 1 distance, where t is the stretch factor. Specifically, we focus on three types of objects: rectilinear segments, axis aligned rectangles, and rectilinear monotone polygons. By combining ideas of t-weekly dominating set, walls, aligned pairs and interval cover, we develop a 4-approximation algorithm (measured by the number of Steiner points) for each type of objects. Our algorithms run in near quadratic time, and can be easily implemented for practical applications. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Zhu, Y., Xu, J., Yang, Y., Katoh, N., & Tanigawa, S. I. (2008). Geometric spanner of objects under L 1 distance. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5092 LNCS, pp. 395–404). https://doi.org/10.1007/978-3-540-69733-6_39
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