Fast algorithms for finding nearest common ancestors
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Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
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ACM Transactions on Programming Languages and Systems (TOPLAS)
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Finding lowest common ancestors in arbitrarily directed trees
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Rectangular matrix multiplication revisited
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Faster algorithms for finding lowest common ancestors in directed acyclic graphs
Theoretical Computer Science
All-pairs disjoint paths from a common ancestor in Õ(nω) time
Theoretical Computer Science
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
Unique lowest common ancestors in dags are almost as easy as matrix multiplication
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Fast lowest common ancestor computations in dags
ESA'07 Proceedings of the 15th annual European conference on Algorithms
LCA queries in directed acyclic graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
All-pairs ancestor problems inweighted dags
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
A scalable approach to computing representative lowest common ancestor in directed acyclic graphs
Theoretical Computer Science
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We develop a path cover technique to solve lowest common ancestor (LCA for short) problems in a directed acyclic graph (dag).Our method yields improved upper bounds for two recently studied problem variants, computing one (representative) LCA for all pairs of vertices and computing all LCAs for all pairs of vertices. The bounds are expressed in terms of the number nof vertices and the so called width w(G) of the input dag G. For the first problem we achieve $\widetilde{O}(n^2 w(G))$ time which improves the upper bound of [18] for dags with w(G) = O( n0.376 茂戮驴 茂戮驴) for a constant 茂戮驴 0. For the second problem our $\widetilde{O}(n^2 w(G)^2)$ upper time bound subsumes the O(n3.334) bound established in [11] for w(G) = O(n0.667 茂戮驴 茂戮驴).As a second major result we show how to combine the path cover technique with LCA solutions for dags with small depth [9]. Our algorithm attains the best known upper time bound for this problem of O(n2.575). However, most notably, the algorithm performs better on a vast amount of input dags, i.e. dags that do not have an almost linear-sized subdag of extremely regular structure.Finally, we apply our technique to improve the general upper time bounds on the worst case time complexity for the problem of reporting LCAs for each triple of vertices recently established by Yuster[26].