Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Randomized algorithms
Influence sets based on reverse nearest neighbor queries
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Space-efficient approximate Voronoi diagrams
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Nearest Neighbors Can Be Found Efficiently If the Dimension Is Small Relative to the Input Size
ICDT '03 Proceedings of the 9th International Conference on Database Theory
Discovery of Influence Sets in Frequently Updated Databases
Proceedings of the 27th International Conference on Very Large Data Bases
Location-based spatial queries
Proceedings of the 2003 ACM SIGMOD international conference on Management of data
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
SWAM: a family of access methods for similarity-search in peer-to-peer data networks
Proceedings of the thirteenth ACM international conference on Information and knowledge management
Supporting spatial aggregation in sensor network databases
Proceedings of the 12th annual ACM international workshop on Geographic information systems
Stabbing the Sky: Efficient Skyline Computation over Sliding Windows
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Adaptive sampling for geometric problems over data streams
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Cluster Hull: A Technique for Summarizing Spatial Data Streams
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Voronoi-based K nearest neighbor search for spatial network databases
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Poster abstract: A distributed algorithm to compute spatial skyline in wireless sensor networks
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
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Several studies have exploited the properties of Voronoi diagrams to improve the efficiency of variations of the nearest neighbor search on stored datasets. However, the significance of Voronoi diagrams and their basic building blocks, Voronoi cells, has been neglected when the geometry data is incrementally becoming available as a data stream. In this paper, we study the problem of Voronoi cell computation for fixed 2-d site points when the locations of the neighboring sites arrive as a spatial data stream. We show that the non-streaming solution to the problem does not meet the memory requirements of many realistic scenarios over a sliding window. Hence, we propose AVC-SW, an approximate streaming algorithm that computes (1 + ε)-approximations to the actual exact Voronoi cell in O(κ) where κ is its sample size. With the sliding window model and random arrival of points, we show both analytically and experimentally that for given window size w and parameter k, AVC-SW reduces the expected memory requirements of the classic algorithm from O(w) to $$O(k \log (\frac{w}{k} + 1))$$ regardless of the distribution of the points in the 2-d space. This is a significant improvement for most of the real-world scenarios where w ≫ k.