Top-k Stabbing Interval Queries

TL;DR

This paper introduces efficient data structures for weighted interval stabbing queries, enabling quick retrieval of top-k heaviest intervals containing a query point, with linear space and optimized query times.

Contribution

It proposes a linear space data structure with $O( ext{log} n + k)$ query time for weighted interval stabbing, and explores alternative trade-offs.

Findings

Linear space data structure for weighted interval stabbing

Query time of $O( ext{log} n + k)$ achieved

Additional trade-offs for the problem are presented

Abstract

We investigate a weighted variant of the interval stabbing problem, where the goal is to design an efficient data structure for a given set $\mathcal{I}$ of weighted intervals such that, for a query point $q$ and an integer $k>0$, we can report the $k$ intervals with largest weights among those stabbed by $q$. In this paper, we present a linear space solution with $O(\log n + k)$ query time. Moreover, we also present another trade-off for the problem.