Hierarchical Categories in Colored Searching

Authors Peyman Afshani, Rasmus Killmann, Kasper Green Larsen



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Author Details

Peyman Afshani
  • Aarhus University, Denmark
Rasmus Killmann
  • Aarhus University, Denmark
Kasper Green Larsen
  • Aarhus University, Denmark

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Peyman Afshani, Rasmus Killmann, and Kasper Green Larsen. Hierarchical Categories in Colored Searching. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ISAAC.2022.25

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Categorical Data
  • Computational Geometry

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