An optimal ancestry scheme and small universal posets

Pierre Fraigniaud, Amos Korman

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

Abstract

In this paper, we solve the ancestry problem, which was introduced more than twenty years ago by Kannan et al. [STOC '88], and is among the most well-studied problems in the field of informative labeling schemes. Specifically, we construct an ancestry labeling scheme for n-node trees with label size log2 n + O(log log n) bits, thus matching the log 2 n + Ω(log log n) bits lower bound given by Alstrup et al. [SODA '03]. Besides its optimal label size, our scheme assigns the labels in linear time, and guarantees that any ancestry query can be answered in constant time. In addition to its potential impact in terms of improving the performances of XML search engines, our ancestry scheme is also useful in the context of partially ordered sets. Specifically, for any fixed integer k, our scheme enables the construction of a universal poset of size O(nk log 4k n) for the family of n-element posets with tree-dimension at most k. This bound is almost tight thanks to a lower bound of nk-o(1) due to Alon and Scheinerman [Order '88].

Original languageEnglish
Title of host publicationSTOC'10 - Proceedings of the 2010 ACM International Symposium on Theory of Computing
Pages611-619
Number of pages9
DOIs
StatePublished - 2010
Externally publishedYes
Event42nd ACM Symposium on Theory of Computing, STOC 2010 - Cambridge, MA, United States
Duration: 5 Jun 20108 Jun 2010

Publication series

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

Conference

Conference42nd ACM Symposium on Theory of Computing, STOC 2010
Country/TerritoryUnited States
CityCambridge, MA
Period5/06/108/06/10

Keywords

  • informative labeling schemes
  • partially ordered sets
  • XML

ASJC Scopus subject areas

  • Software

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