Linear-Space Data Structures for Range Mode Query in Arrays

Low Space Data Structures for Geometric Range Mode Query

Let S be a set of n points in an [n] grid, such that each point is assigned a color. Given a query range Q = [a1, b1] × [a2, b2] × . . . × [ad, bd], the geometric range mode query problem asks to report the most frequent color (i.e., a mode) of the multiset of colors corresponding to points in S ∩ Q. When d = 1, Chan et al. (STACS 2012 [2]) gave a data structure that requires O(n + (n/∆)/w) wor...

Data Structures for Reporting Extension Violations in a Query Range

Design Rule Checking (DRC) in VLSI design involves checking if a given VLSI layout satisfies a given set of rules, and reporting the violations if any. We propose data structures for reporting violations of the minimum extension rule in a query window of

A Simple Linear-Space Data Structure for Constant-Time Range Minimum Query

We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution that is simple, intuitive, and practical without increasing asymptotic costs for query time or space.

Space Efficient Data Structures for Dynamic Orthogonal Range Counting

We present a linear-space data structure that maintains a dynamic set of n points with coordinates of real numbers on the plane to support orthogonal range counting, as well as insertions and deletions, in O(( lgn lg lgn )) time. This provides faster support for updates than previous results with the same bounds on space cost and query time. We also obtain two other new results by considering t...

An efficient algorithm for hyperspherical range query processing in high-dimensional data space