Given a set P of coloured points on the real line, we study the problem of
answering range α-majority (or "heavy hitter") queries on P. More
specifically, for a query range Q, we want to return each colour that is
assigned to more than an α-fraction of the points contained in Q. We
present a new data structure for answering range α-majority queries on a
dynamic set of points, where α∈(0,1). Our data structure uses O(n)
space, supports queries in O((lgn)/α) time, and updates in O((lgn)/α) amortized time. If the coordinates of the points are integers,
then the query time can be improved to O(lgn/(αlglgn)+(lg(1/α))/α)). For constant values of α, this improved query
time matches an existing lower bound, for any data structure with
polylogarithmic update time. We also generalize our data structure to handle
sets of points in d-dimensions, for d≥2, as well as dynamic arrays, in
which each entry is a colour.Comment: 16 pages, Preliminary version appeared in ISAAC 201