SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Smooth view-dependent level-of-detail control and its application to terrain rendering
Proceedings of the conference on Visualization '98
A road network embedding technique for k-nearest neighbor search in moving object databases
Proceedings of the 10th ACM international symposium on Advances in geographic information systems
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Digital Image Processing: PIKS Scientific Inside
Digital Image Processing: PIKS Scientific Inside
Scalable network distance browsing in spatial databases
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
A multi-resolution surface distance model for k-NN query processing
The VLDB Journal — The International Journal on Very Large Data Bases
Indexing land surface for efficient kNN query
Proceedings of the VLDB Endowment
Reducing the memory required to find a geodesic shortest path on a large mesh
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Continuous monitoring of nearest neighbors on land surface
Proceedings of the VLDB Endowment
Path oracles for spatial networks
Proceedings of the VLDB Endowment
Monochromatic and bichromatic reverse nearest neighbor queries on land surfaces
Proceedings of the 21st ACM international conference on Information and knowledge management
A framework of traveling companion discovery on trajectory data streams
ACM Transactions on Intelligent Systems and Technology (TIST) - Special Section on Intelligent Mobile Knowledge Discovery and Management Systems and Special Issue on Social Web Mining
| Hi-index | 0.00 |
The growing popularity of online Earth visualization tools and geo-realistic games and the availability of high resolution terrain data have motivated a new class of queries to the interests of the GIS and spatial database community: spatial queries (e.g., kNN) over land surface. However, the fundamental challenges that restrict the applicability of these studies to real world applications are the prohibitive time complexity and storage overhead to precompute the shortest surface paths. In this paper, for the first time, we propose an approximate solution to address both challenges and allow browsing the shortest surface paths in O(log N + √N) time, where N is the size of the terrain. With this method, the time and space requirements for an exhaustive all-pair pre-computation have been reduced from O(N3) to O(N1.5) and O(N) respectively. The substantial savings in both time and storage are gained by taking advantage of the fact that the O(N2) surface paths only deviate from approximate straight lines at O(√N) points, termed rough vertices. As a result, we propose a linear time shortest surface path computation algorithm between two arbitrary vertices and a linear size storage structure, which captures all the shortest surface paths between any pair of vertices. We experimentally verified the applicability and scalability of the proposed methods with large real world and synthetic data sets and showed that accuracy higher than 97% can be obtained in most cases.