Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Approximating the complete Euclidean graph
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Optimally sparse spanners in 3-dimensional Euclidean space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A fast algorithm for constructing sparse Euclidean spanners
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
Optimal spanners for axis-aligned rectangles
Computational Geometry: Theory and Applications
Randomized and deterministic algorithms for geometric spanners of small diameter
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Geometric Spanner of Objects under L1 Distance
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
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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 a generalization of the classical geometric spanner problem (called segment spanner): Given a set S of disjoint 2-D segments, find a spanning network G with minimum size so that for any pair of points in S, there exists a path in G with length no more than t times their Euclidean distance. Based on a number of interesting techniques (such as weakly dominating set, strongly dominating set, and interval cover), we present an efficient algorithm to construct the segment spanner. Our approach first identifies a set of Steiner points in S, then construct a point spanner for them. Our algorithm runs in O(|Q| + n2 log n) time, where Q is the set of Steiner points. We show that Q is an O(1)-approximation in terms of its size when S is relatively "well" separated by a constant. For arbitrary rectilinear segments under L1 distance, the approximation ratio improves to 2.