An efficient algorithm for the 1D total visibility-index problem and its parallelization
| Autor: | Henri Casanova, Peyman Afshani, Mark de Berg, Constantinos Tsirogiannis, Ben Karsin, Colin Lambrechts, Nodari Sitchinava |
|---|---|
| Přispěvatelé: | Algorithms, Geometry and Applications |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Geographic information system
Computer science business.industry Parallel algorithms Line segment intersection 0211 other engineering and technologies Parallel algorithm Terrain 0102 computer and information sciences 02 engineering and technology Parallel computing 01 natural sciences Computational geometry Theoretical Computer Science Counting problem 010201 computation theory & mathematics Persistent data structures Terrain visibility Leverage (statistics) Persistent data structure business Implementation 021101 geological & geomatics engineering |
| Zdroj: | Journal on Experimental Algorithmics, 23(2):2.3. Association for Computing Machinery, Inc Afshani, P, De Berg, M, Casanova, H, Karsin, B, Lambrechts, C, Sitchinava, N & Tsirogiannis, C 2018, ' An efficient algorithm for the 1D total visibility-index problem and its parallelization ', ACM Journal of Experimental Algorithmics, vol. 23, 2.3 . https://doi.org/10.1145/3209685 |
| ISSN: | 1084-6654 |
| DOI: | 10.1145/3209685 |
| Popis: | Let T be a terrain and P be a set of points on its surface. An important problem in Geographic Information Science (GIS) is computing the visibility index of a point p on P , that is, the number of points in P that are visible from p . The total visibility-index problem asks for the visibility index of every point in P . We present the first subquadratic-time algorithm to solve the one-dimensional total-visibility-index problem. Our algorithm uses a geometric dualization technique to reduce the problem to a set of instances of the red--blue line segment intersection counting problem, allowing us to find the total visibility-index in O ( n log 2 n ) time. We implement a naive O ( n 2 ) approach and four variations of our algorithm: one that uses an existing red--blue line segment intersection counting algorithm and three new approaches that leverage features specific to our problem. Two of our implementations allow for parallel execution, requiring O (log 2 n ) time and O ( n log 2 n ) work in the CREW PRAM model. We present experimental results for both serial and parallel implementations on synthetic and real-world datasets using two hardware platforms. Results show that all variants of our algorithm outperform the naive approach by several orders of magnitude. Furthermore, we show that our special-case red--blue line segment intersection counting implementations out-perform the existing general-case solution by up to a factor 10. Our fastest parallel implementation is able to process a terrain of more than 100 million vertices in under 3 minutes, achieving up to 85% parallel efficiency using 16 cores. |
| Databáze: | OpenAIRE |
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