Dynamic 3-Sided Planar Range Queries with Expected Doubly Logarithmic Time

Authors:
Gerth Stølting Brodal;Alexis C. Kaporis;Spyros Sioutas;Konstantinos Tsakalidis;Kostas Tsichlas
Affiliations:
MADALGO, Department of Computer Science, Aarhus University, Denmark;Computer Engineering and Informatics Department, University of Patras, Greece;Department of Informatics, Ionian University, Corfu, Greece;MADALGO, Department of Computer Science, Aarhus University, Denmark;Department of Informatics, Aristotle University of Thessaloniki, Greece
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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Abstract

We consider the problem of maintaining dynamically a set of points in the plane and supporting range queries of the type [a,b]脳( 驴驴 , c]. We assume that the inserted points have their x-coordinates drawn from a class of smooth distributions, whereas the y-coordinates are arbitrarily distributed. The points to be deleted are selected uniformly at random among the inserted points. For the RAM model, we present a linear space data structure that supports queries in O(loglogn + t) expected time with high probability and updates in O(loglogn) expected amortized time, where n is the number of points stored and t is the size of the output of the query. For the I/O model we support queries in O(loglog B n + t/B) expected I/Os with high probability and updates in O(log B logn) expected amortized I/Os using linear space, where B is the disk block size. The data structures are deterministic and the expectation is with respect to the input distribution.