36,900 research outputs found
Near-optimal labeling schemes for nearest common ancestors
We consider NCA labeling schemes: given a rooted tree , label the nodes of
with binary strings such that, given the labels of any two nodes, one can
determine, by looking only at the labels, the label of their nearest common
ancestor.
For trees with nodes we present upper and lower bounds establishing that
labels of size , are both sufficient and
necessary. (All logarithms in this paper are in base 2.)
Alstrup, Bille, and Rauhe (SIDMA'05) showed that ancestor and NCA labeling
schemes have labels of size . Our lower bound
increases this to for NCA labeling schemes. Since
Fraigniaud and Korman (STOC'10) established that labels in ancestor labeling
schemes have size , our new lower bound separates
ancestor and NCA labeling schemes. Our upper bound improves the
upper bound by Alstrup, Gavoille, Kaplan and Rauhe (TOCS'04), and our
theoretical result even outperforms some recent experimental studies by Fischer
(ESA'09) where variants of the same NCA labeling scheme are shown to all have
labels of size approximately
Efficient parallel algorithms for a class of graph theoretic problems
The authors present efficient parallel algorithms for the following graph problems: finding the lowest common ancestors for vertex pairs of a directed tree; finding all fundamental cycles, a directed spanning forest, all bridges, all bridge-connected components, all separation vertices, all biconnected components, and testing the biconnectivity of an undirected graph. All these algorithms achieve the O(lg**2n) time bound.published_or_final_versio
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