Dynamic planar point location with sub-logarithmic local updates

Authors:
Maarten Löffler;Joseph A. Simons;Darren Strash
Affiliations:
Dept. of Information and Computing Sciences, Utrecht University, Italy;Dept. of Computer Science, University of California, Irvine;Dept. of Computer Science, University of California, Irvine
Venue:
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Year:
2013

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Abstract

We study planar point location in a collection of disjoint fat regions, and investigate the complexity of local updates: replacing any region by a different region that is "similar" to the original region. (i.e., the size differs by at most a constant factor, and distance between the two regions is a constant times that size).We show that it is possible to create a linear size data structure that allows for insertions, deletions, and queries in logarithmic time, and allows for local updates in sub-logarithmic time on a pointer machine. We also give results parameterized by the fatness and similarity of the objects considered.