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Data structure set-trie for storing and querying sets: Theoretical and empirical analysis.

Iztok Savnik1,2, Mikita Akulich1, Matjaž Krnc1,2,3

  • 1Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Koper, Slovenia.

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Summary

This study introduces the set-trie data structure for efficient set containment operations. Set-trie significantly outperforms the inverted index, especially for datasets with low cardinality sets.

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Area of Science:

  • Computer Science
  • Data Structures
  • Algorithms

Background:

  • Set containment operations are crucial for information retrieval, AI, and database systems.
  • Existing data structures may not efficiently handle large-scale set operations.

Purpose of the Study:

  • To introduce and analyze the set-trie data structure for efficient set containment operations.
  • To evaluate the performance of set-trie through mathematical and empirical studies.

Main Methods:

  • Developed and analyzed a set-trie data structure.
  • Conducted mathematical analysis using probabilistic models to establish performance bounds.
  • Performed empirical studies on randomly generated and real-world datasets.
  • Compared set-trie performance against the inverted index.

Main Results:

  • Established upper-bounds on the expected performance of set-trie.
  • Identified key sources of input sensitivity in set-trie performance.
  • Set-trie consistently outperformed the inverted index by orders of magnitude on real-world datasets with low cardinality sets.

Conclusions:

  • Set-trie is a highly efficient data structure for set containment operations.
  • The performance of set-trie is robust and significantly better than the inverted index for specific data types.