The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Computational geometry: an introduction
Computational geometry: an introduction
Sorting Jordan sequences in linear time using level-linked search trees
Information and Control
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Determining an optimal penetration among weighted regions in two and three dimensions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Shortest paths in an arrangement with k line orientations
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Plane-sweep algorithms for intersecting geometric figures
Communications of the ACM
Fast implementation of depth contours using topological sweep
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On Some Geometric Optimization Problems in Layered Manufacturing
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
An Efficient Algorithm for Shortest Paths in Vertical and Horizontal Segments
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Topological Sweeping in Three Dimensions
SIGAL '90 Proceedings of the International Symposium on Algorithms
Finding an Optimal Path without Growing the Tree
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Approximating Shortest Paths in Arrangements of Lines
Proceedings of the 8th Canadian Conference on Computational Geometry
| Hi-index | 0.00 |
We present a new approach, called topological peeling, and its implementation for traversing a portion AR of the arrangement formed by n lines within a convex region R on the plane. Topological peeling visits the cells of AR in a fashion of propagating a "wave" of a special shape (called a double-wriggle curve) starting at a single source point. This special traversal fashion enables us to solve several problems (e.g., computing shortest paths) on planar arrangements to which previously best known arrangement traversal techniques such as topological sweep and topological walkm ay not be directly applicable. Our topological peeling algorithm takes O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells in AR and r is the number of boundary vertices of R. Comparing with topological walk, topological peeling uses a simpler and more efficient way to sweep different types of lines, and relies heavily on exploring small local structures, rather than a much larger global structure. Experiments show that, on average, topological peeling outperforms topological walk by 10-15% in execution time.