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Hierarchical Categories in Colored Searching

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

In colored range counting (CRC), the input is a set of points where each point is assigned a “color” (or a “category”) and the goal is to store them in a data structure such that the number of distinct categories inside a given query range can be counted efficiently. CRC has strong motivations as it allows data structure to deal with categorical data. However, colors (i.e., the categories) in the CRC problem do not have any internal structure, whereas this is not the case for many datasets in practice where hierarchical categories exists or where a single input belongs to multiple categories. Motivated by these, we consider variants of the problem where such structures can be represented. We define two variants of the problem called hierarchical range counting (HCC) and sub-category colored range counting (SCRC) and consider hierarchical structures that can either be a DAG or a tree. We show that the two problems on some special trees are in fact equivalent to other well-known problems in the literature. Based on these, we also give efficient data structures when the underlying hierarchy can be represented as a tree. We show a conditional lower bound for the general case when the existing hierarchy can be any DAG, through reductions from the orthogonal vectors problem.

Original languageEnglish
Title of host publication33rd International Symposium on Algorithms and Computation, ISAAC 2022
EditorsSang Won Bae, Heejin Park
Number of pages15
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication yearDec 2022
Article number25
ISBN (Electronic)9783959772587
Publication statusPublished - Dec 2022
Event33rd International Symposium on Algorithms and Computation, ISAAC 2022 - Virtual, Online, Korea, Republic of
Duration: 19 Dec 202221 Dec 2022


Conference33rd International Symposium on Algorithms and Computation, ISAAC 2022
LandKorea, Republic of
ByVirtual, Online
SeriesLeibniz International Proceedings in Informatics, LIPIcs

Bibliographical note

Publisher Copyright:
© Peyman Afshani, Rasmus Killmann, and Kasper Green Larsen.

    Research areas

  • Categorical Data, Computational Geometry

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