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Kinetic k-Semi-Yao graph and its applications

Rahmati, Z ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1016/j.comgeo.2015.11.001
  3. Publisher: Elsevier B.V , 2019
  4. Abstract:
  5. This paper introduces a new supergraph, called the k-Semi-Yao graph (k-SYG), of the k-nearest neighbor graph (k-NNG) of a set P of points in Rd. We provide a kinetic data structure (KDS) to maintain the k-SYG on moving points, where the trajectory of each point is a polynomial function whose degree is bounded by some constant. Our technique gives the first KDS for the theta graph (i.e., 1-SYG) in Rd. It generalizes and improves on previous work on maintaining the theta graph in R2. As an application, we use the kinetic k-SYG to provide the first KDS for maintenance of all the k-nearest neighbors in Rd, for any k≥1. Previous works considered the k=1 case only. Our KDS for all the 1-nearest neighbors is deterministic. The best previous KDS for all the 1-nearest neighbors in Rd is randomized. Our structure and analysis are simpler and improve on this work for the k=1 case. We also provide a KDS for all the (1+ϵ)-nearest neighbors, which in fact gives better performance than previous KDSs for maintenance of all the exact 1-nearest neighbors. As another application, we present the first KDS for answering reverse k-nearest neighbor queries on moving points in Rd, for any k≥1
  6. Keywords:
  7. Continuous monitoring ; Continuous queries ; k-Nearest neighbors ; Kinetic data structure ; Reverse k-nearest neighbor queries ; Data structures ; Kinetics ; Membership functions ; Motion compensation ; Text processing ; Reverse k-nearest neighbors ; Nearest neighbor search
  8. Source: Computational Geometry: Theory and Applications ; Volume 77 , 2019 , Pages 10-26 ; 09257721 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0925772115001248