Compact labeling schemes for ancestor queries
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Informative Labeling Schemes for Graphs
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
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This paper introduces the notion of informative labeling schemes for arbitrary graphs. Let f(W) be a function on subsets of vertices W. An f labeling scheme labels the vertices of a weighted graph G in such a way that f(W) can be inferred (or at least approximated) efficiently for any vertex subset W of G by merely inspecting the labels of the vertices of W, without having to use any additional information sources. A number of results illustrating this notion are presented in the paper. We begin by developing f labeling schemes for three functions f over the class of n-vertex trees. The first function, SepLevel, gives the separation level of any two vertices in the tree, namely, the depth of their least common ancestor. The second, LCA, provides the least common ancestor of any two vertices. The third, Center, yields the center of any three given vertices vsub/subsub/subsub/sub