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Suppose we have two trees on the same set of leaves, in which nodes areweighted such that children are heavier than their parents. We say a node fromthe first tree and a node from the second tree are induced together if theyhave a common leaf descendant. In this paper we describe data structures thatefficiently support the following heaviest-induced-ancestor query: given a nodefrom the first tree and a node from the second tree, find an induced pair oftheir ancestors with maximum combined weight. Our solutions are based on ageometric interpretation that enables us to find heaviest induced ancestorsusing range queries. We then show how to use these results to build anLZ-compressed index with which we can quickly find with high probability alongest substring common to the indexed string and a given pattern.

Heaviest Induced Ancestors and Longest Common Substrings