Compact Labeling Scheme for Ancestor Queries

We consider the following problem. Given a rooted tree T , label the nodes of T in the most compact way such that given the labels of two nodes u and v one can determine in constant time, by looking only at the labels, if u is ancestor of v. The best known labeling scheme is rather straightforward and uses labels of length at most 2 log2 n bits each, where n is the number of nodes in the tree. Our main result in this paper is a labeling scheme with maximum label length log2 n + O( √ log n). Our motivation for studying this problem is enhancing the performance of web search engines. In the context of this application each indexed document is a tree and the labels of all trees are maintained in main memory. Therefore even small improvements in the maximum label length are important.