A Ptolemaic partitioning mechanism

Richard Connor*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

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For many years, exact metric search relied upon the property of triangle inequality to give a lower bound on uncalculated distances. Two exclusion mechanisms derive from this property, generally known as pivot exclusion and hyperplane exclusion. These mechanisms work in any proper metric space and are the basis of many metric indexing mechanisms. More recently, the Ptolemaic and four-point lower bound properties have been shown to give tighter bounds in some subclasses of metric space. Both triangle inequality and the four-point lower bound directly imply straightforward partitioning mechanisms: that is, a method of dividing a finite space according to a fixed partition, in order that one or more classes of the partition can be eliminated from a search at query time. However, up to now, no partitioning principle has been identified for the Ptolemaic inequality, which has been used only as a filtering mechanism. Here, a novel partitioning mechanism for the Ptolemaic lower bound is presented. It is always better than either pivot or hyperplane partitioning. While the exclusion condition itself is weaker than Hilbert (four-point) exclusion, its calculation is cheaper. Furthermore, it can be combined with Hilbert exclusion to give a new maximum for exclusion power with respect to the number of distances measured per query.
Original languageEnglish
Title of host publicationSimilarity Search and Applications
Subtitle of host publication15th International Conference, SISAP 2022, Bologna, Italy, October 5–7, 2022, Proceedings
EditorsTomáš Skopal, Fabrizio Falchi, Jakub Lokoč, Maria Luisa Sapino, Ilaria Bartolini, Marco Patella
Place of PublicationCham
PublisherSpringer, Cham
Number of pages14
ISBN (Electronic)9783031178498
ISBN (Print)9783031178481
Publication statusPublished - 28 Sept 2022
EventInternational Conference on Similarity Search and Applications, SISAP 2022 - Bologna, Italy
Duration: 5 Oct 20227 Oct 2022
Conference number: 15

Publication series

NameLecture notes in computer science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceInternational Conference on Similarity Search and Applications, SISAP 2022
Abbreviated titleSISAP 2022
Internet address


  • Metric search
  • Partitioning
  • Ptolemaic inequality
  • Supermetric space


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