Fast Lowest Common Ancestor Computations in Dags

Eckhardt, Stefan; Mühling, Andreas; Nowak, Johannes

doi:10.1007/978-3-540-75520-3_62

Cited by 16 publications

(12 citation statements)

References 22 publications

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“…Eckhardt et al [9] show that the expected number of edges in a transitively reduced digraph is Θ(n log n) in a random graph model where each edge is included in the graph with probability p. Our model for generating the graphs is somewhat different, but leads to the same asymptotic bound. There is a clear bijection between any permutation on n elements and a two-dimensional partial order of n elements.…”

Section: Methodsmentioning

confidence: 82%

Confluent Hasse Diagrams

Eppstein¹,

Simons²

2013

JGAA

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We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with O(n 2 ) features, in an O(n) × O(n) grid in O(n 2 ) time. For the digraphs representing series-parallel partial orders we show how to construct a drawing with O(n) features in an O(n) × O(n) grid in O(n) time from a series-parallel decomposition of the partial order. Our drawings are optimal in the number of confluent junctions they use.

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Section: Methodsmentioning

confidence: 82%

Confluent Hasse Diagrams

Eppstein¹,

Simons²

2013

JGAA

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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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“…A direct use of matrix multiplication leads to a high polynomial (n 6 ) time complexity. Therefore, it is simpler and more efficient to use an algorithm based on the transitive closure mechanism, see For non-constant k, the algorithm finding for each pair all its LCAs is more efficient, see [5].…”

Section: Finding K-lcasmentioning

confidence: 99%