Hierarchical Categories in Colored Searching
Peyman Afshani, Rasmus Killman, Kasper Green Larsen

TL;DR
This paper introduces hierarchical variants of colored range counting, enabling efficient querying of categories with internal structure, and provides data structures and complexity bounds for these problems.
Contribution
It defines hierarchical range counting and sub-category colored range counting, analyzes their complexity, and develops efficient data structures for tree hierarchies, extending CRC to structured categories.
Findings
Special cases are equivalent to known problems.
Efficient data structures are proposed for tree hierarchies.
Conditional lower bounds are established for DAG hierarchies.
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…
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Taxonomy
TopicsAdvanced Image and Video Retrieval Techniques · Constraint Satisfaction and Optimization · Data Management and Algorithms
