Independent range sampling, revisited again

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer k, we can extract k independent random samples from the points inside the query range, where the probability of sampling a point is proportional to its weight. This line of work was initiated in 2014 by Hu, Qiao, and Tao and it was later followed up by Afshani and Wei. The first line of work mostly studied unweighted but dynamic version of the problem in one dimension whereas the second result considered the static weighted problem in one dimension as well as the unweighted problem in 3D for halfspace queries. We offer three main results and some interesting insights that were missed by the previous work: We show that it is possible to build efficient data structures for range sampling queries if we allow the query time to hold in expectation (the first result), or obtain efficient worst-case query bounds by allowing the sampling probability to be approximately proportional to the weight (the second result). The third result is a conditional lower bound that shows essentially one of the previous two concessions is needed. For instance, for the 3D range sampling queries, the first two results give efficient data structures with near-linear space and polylogarithmic query time whereas the lower bound shows with near-linear space the worst-case query time must be close to n2/3, ignoring polylogarithmic factors. Up to our knowledge, this is the first such major gap between the expected and worst-case query time of a range searching problem.

Original languageEnglish
Title of host publication35th International Symposium on Computational Geometry, SoCG 2019
EditorsGill Barequet, Yusu Wang
Number of pages13
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication year2019
Article number4
ISBN (Electronic)9783959771047
DOIs
Publication statusPublished - 2019
Event35th International Symposium on Computational Geometry, SoCG 2019 - Portland, United States
Duration: 18 Jun 201921 Jun 2019

Conference

Conference35th International Symposium on Computational Geometry, SoCG 2019
LandUnited States
ByPortland
Periode18/06/201921/06/2019
SeriesLeibniz International Proceedings in Informatics, LIPIcs
Volume129
ISSN1868-8969

    Research areas

  • Data structures, Range searching, Sampling

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