All-Pairs Ancestor Problems in Weighted Dags

Baumgart, Matthias; Eckhardt, Stefan; Griebsch, Jan; Kosub, Sven; Nowak, Johannes

doi:10.1007/978-3-540-74450-4_26

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Cited by 9 publications

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“…The first contribution of this article is summarized in the following theorem. This should be directly compared to the LCA-schemes in dags [3,4,6,7,14,15], which have at least three computational drawbacks:…”

Section: Our Resultsmentioning

confidence: 99%

New common ancestor problems in trees and directed acyclic graphs

Fischer

Huson

2010

Information Processing Letters

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We derive a new generalization of lowest common ancestors (LCAs) in dags, called the lowest single common ancestor (LSCA). We show how to preprocess a static dag in linear time such that subsequent LSCA-queries can be answered in constant time. The size is linear in the number of nodes. We also consider a "fuzzy" variant of LSCA that allows to compute a node that is only an LSCA of a given percentage of the query nodes. The space and construction time of our scheme for fuzzy LSCAs is linear, whereas the query time has a sub-logarithmic slow-down. This "fuzzy" algorithm is also applicable to LCAs in trees, with the same complexities.

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