TY - GEN
T1 - Geometric spanner of objects under L 1 distance
AU - Zhu, Yongding
AU - Xu, Jinhui
AU - Yang, Yang
AU - Katoh, Naoki
AU - Tanigawa, Shin Ichi
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/48249133937
U2 - 10.1007/978-3-540-69733-6_39
DO - 10.1007/978-3-540-69733-6_39
M3 - Conference contribution
SN - 3540697322
SN - 9783540697329
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 395
EP - 404
BT - Computing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings
T2 - 14th Annual International Conference on Computing and Combinatorics, COCOON 2008
Y2 - 27 June 2008 through 29 June 2008
ER -