Range mode and range median queries in constant time and sub-quadratic space

Authors:
Holger Petersen;Szymon Grabowski
Affiliations:
Universität Stuttgart, FMI, Universitätsstr. 38, D-70569 Stuttgart, Germany;Technical University of Łódź, Computer Engineering Department, Al. Politechniki 11, 90-924 Łódź, Poland
Venue:
Information Processing Letters
Year:
2009

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Abstract

Given a list of n items and a function defined over sub-lists, we study the space required for computing the function for arbitrary sub-lists in constant time. For the function mode we improve the previously known space bound O(n^2/logn) to O(n^2loglogn/log^2n) words. For median the space bound is improved to O(n^2loglog^2n/log^2n) words from O(n^2@?log^(^k^)n/logn), where k is an arbitrary constant and log^(^k^) is the iterated logarithm.