Improved labeling scheme for ancestor queries

  • Authors:
  • Stephen Alstrup;Theis Rauhe

  • Affiliations:
  • IT University in Copenhagen, Glentevej 67, DK-2400 Copenhagen NV, Denmark;IT University in Copenhagen, Glentevej 67, DK-2400 Copenhagen NV, Denmark

  • Venue:
  • SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2002

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Abstract

We present a labeling scheme for rooted trees that supports ancestor queries. Given a tree, the scheme assigns to each node a label which is a binary string. Given the labels of any two nodes u and v, it can in constant time be determined whether u is ancestor to v alone from these labels. For trees of size n our scheme assigns labels of size bounded by log n + O(√log n) bits to each node. This improves a recent result of Abiteboul, Kaplan and Milo at SODA'01, where a labeling scheme with labels of size 3/2log n + O(log log n) was presented. The problem is among other things motivated in connection with efficient representation of information for XML-based search engines for the internet.