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arXiv · 1305.3164

Heaviest Induced Ancestors and Longest Common Substrings

Travis Gagie·Paweł Gawrychowski·Yakov Nekrich
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Abstract

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

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Travis Gagie, Paweł Gawrychowski, Yakov Nekrich. 2013-05-14. Heaviest Induced Ancestors and Longest Common Substrings. https://arxiv.org/abs/1305.3164

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