Prioritized metric structures and embedding

Michael Elkin, Arnold Filtser, Ofer Neiman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations


Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms, online algorithms, distributed algorithms and for computing sparsifiers. However, this methodology appears to have a limitation: the worst-case performance inherently depends on the cardinality of the metric, and one could not specify in advance which vertices/points should enjoy a better service (i.e., stretch/distortion, label size/dimension) than that given by the worst-case guarantee. In this paper we alleviate this limitation by devising a suit of prioritized metric data structures and embeddings. We show that given a priority ranking (x1,x2, . . . ,xn) of the graph vertices (respectively, metric points) one can devise a metric data structure (respectively, embedding) in which the stretch (resp., distortion) incurred by any pair containing a vertex xj will depend on the rank j of the vertex. We also show that other important parameters, such as the label size and (in some sense) the dimension, may depend only on j. In some of our metric data structures (resp., embeddings) we achieve both prioritized stretch (resp., distortion) and label size (resp., dimension) simultaneously. The worst-case performance of our metric data structures and embeddings is typically asymptotically no worse than of their non-prioritized counterparts.

Original languageEnglish
Title of host publicationSTOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Electronic)9781450335362
StatePublished - 14 Jun 2015
Externally publishedYes
Event47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States
Duration: 14 Jun 201517 Jun 2015

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/TerritoryUnited States


  • Distance oracles
  • Metric embedding
  • Priorities
  • Routing


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