2 research outputs found
Kinetic Reverse -Nearest Neighbor Problem
This paper provides the first solution to the kinetic reverse -nearest
neighbor (\rknn) problem in , which is defined as follows: Given
a set of moving points in arbitrary but fixed dimension , an integer
, and a query point at any time , report all the points for which is one of the -nearest neighbors of
Kinetic -Semi-Yao Graph and its Applications
This paper introduces a new proximity graph, called the -Semi-Yao graph
(-SYG), on a set of points in , which is a supergraph of
the -nearest neighbor graph (-NNG) of . We provide a kinetic data
structure (KDS) to maintain the -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 (\ie, -SYG)
in . It generalizes and improves on previous work on maintaining
the theta graph in .
As an application, we use the kinetic -SYG to provide the first KDS for
maintenance of all the -nearest neighbors in , for any . Previous works considered the case only. Our KDS for all the
-nearest neighbors is deterministic. The best previous KDS for all the
-nearest neighbors in is randomized. Our structure and
analysis are simpler and improve on this work for the case. We also
provide a KDS for all the -nearest neighbors, which in fact gives
better performance than previous KDS's for maintenance of all the exact
-nearest neighbors.
As another application, we present the first KDS for answering reverse
-nearest neighbor queries on moving points in , for any
.Comment: arXiv admin note: text overlap with arXiv:1307.2700, arXiv:1406.555