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Encoding Data Structures for Range Queries on Arrays

Authors Seungbum Jo , Srinivasa Rao Satti

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ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • range queries
  • RMQ
  • Cartesian tree
  • top-k queries
  • range median
  • range mode

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Abstract

Efficiently processing range queries on arrays is a fundamental problem in computer science, with applications spanning diverse domains such as database management, computational biology, and geographic information systems. A range query retrieves information about a specific segment of an array, such as the sum, minimum, maximum, or median of elements within a given range. The challenge lies in designing data structures that allow such queries to be answered quickly, often in constant or logarithmic time, while keeping space overhead (and preprocessing time) small. Encoding data structures for range queries has emerged as a pivotal area of research due to the increasing demand for high-performance systems handling massive datasets. These structures consider the data together with the queries and aim to store only as much information about the data as is needed to answer the queries. The data structure does not need to access the original data to answer the queries. Encoding-based solutions often leverage techniques from succinct data structures, bit manipulation, and combinatorial optimization to achieve both space and time efficiency. By encoding the array in a manner that preserves critical information, these methods strike a balance between query time and space usage. In this survey article, we explore the landscape of encoding data structures for range queries on arrays, providing a comprehensive overview of some important results on space-efficient encodings for various types of range query.

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Seungbum Jo and Srinivasa Rao Satti. Encoding Data Structures for Range Queries on Arrays. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 12:1-12:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Grossi.12

Author Details

Seungbum Jo
  • Chungnam National University, Daejeon, South Korea
Srinivasa Rao Satti
  • Norwegian University of Science and Technology, Trondheim, Norway

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