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
Efficient and small representation of line arrangements with applications
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
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
Topological Peeling and Implementation
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
| Hi-index | 0.00 |
In this paper, we present an experimental study comparing two algorithms, topological peeling and topological walk, for traversing arrangements of planar lines. Given a set H of n lines and a convex region R on a plane, both topological peeling and topological walk sweep the portion AR of the arrangement of H inside R in O(K + n log(n + r)) time and O(n + r) space, where K is the number of cells of AR and r is the number of boundary vertices of R. In our study, we robustly implemented these two algorithms using the LEDA library. Based on the implementation, we carried out experiments to conduct several comparisons, such as the arrangement traversal fashions, memory consumption, and execution time. In general, topological peeling exhibits a better control on the propagation of its sweeping curve (called the wavefront). For memory consumption, two types of measures, logical and physical memory, were examined. Our experiments showed that although both algorithms use nearly the same amount of logical memory, topological peeling could use twice as much physical memory as topological walk. For execution time, experiments revealed an interesting phenomenon that topological peeling has a 10% to 25% faster execution time than topological walk in most cases. Our analysis of this phenomenon indicates that the execution times of topological peeling and topological walk are both sensitive to the ratio of the lower input lines to all input lines. When the ratio of the lower lines to all input lines is around 85%, the two algorithms have roughly the same amount of execution time. Under this ratio, topological peeling considerably outperforms topological walk; above this ratio, topological walk slightly outperforms topological peeling.