Labeling schemes for small distances in trees

Authors:
Stephen Alstrup;Philip Bille;Theis Rauhe
Affiliations:
IT University of Copenhagen, Glentevej 67, Copenhagen NV, Denmark;IT University of Copenhagen, Glentevej 67, Copenhagen NV, Denmark;IT University of Copenhagen, Glentevej 67, Copenhagen NV, Denmark
Venue:
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2003

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Abstract

We consider labeling schemes for trees, supporting various relationships between nodes at small distance. For instance, we show that given a tree T and an integer k we can assign labels to each node of T such that given the label of two nodes we can decide, from these two labels alone, if the distance between v and w is at most k and if so compute it. For trees with n nodes and k ≥ 2, we give a lower bound on the maximum label length of log n + Ω(log log n) bits, and for constant k, we give an upper bound of log n + O(log log n). Bounds for ancestor, sibling, connectivity and bi- and triconnectivity labeling schemes are also presented.