Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Efficient implementation of lattice operations
ACM Transactions on Programming Languages and Systems (TOPLAS)
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Finding lowest common ancestors in arbitrarily directed trees
Information Processing Letters
New algorithms for the LCA problem and the binary tree reconstruction problem
Information Processing Letters
Finding level-ancestors in trees
Journal of Computer and System Sciences
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Rectangular matrix multiplication revisited
Journal of Complexity
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
The lowest common ancestor problem on a tree with an unfixed root
Information Sciences: an International Journal
Finding least common ancestors in directed acyclic graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On inferring autonomous system relationships in the internet
IEEE/ACM Transactions on Networking (TON)
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Dilworth's Theorem and Its Application for Path Systems of a Cycle - Implementation and Analysis
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Phylogenetic Networks: Modeling, Reconstructibility, and Accuracy
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
SIAM Journal on Computing
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
LCA queries in directed acyclic graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Phylogenetic networks: properties and relationship to trees and clusters
Transactions on Computational Systems Biology II
A Path Cover Technique for LCAs in Dags
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
New common ancestor problems in trees and directed acyclic graphs
Information Processing Letters
Fast lowest common ancestor computations in dags
ESA'07 Proceedings of the 15th annual European conference on Algorithms
A scalable approach to computing representative lowest common ancestor in directed acyclic graphs
Theoretical Computer Science
Hi-index | 0.00 |
This work studies (lowest) common ancestor problems in (weighted) directed acyclic graphs. We improve previous algorithms for the all-pairs representative LCA problem to O(n2.575) by using fast rectangular matrix multiplication. We prove a first non-trivial upper bound of O(min{n2m, n3.575}) for the all-pairs all lowest common ancestors problem. Furthermore, classes of dags are identified for which the problem can be solved considerably faster. Our algorithms scale with the maximal number of LCAs for one pair and--based on the famous Dilworth's theorem--with the size of a maximum antichain (i.e., width) of the dag. We extend and generalize previous results on computing shortest ancestral distances. It is shown that finding shortest distance common ancestors in weighted dags is not harder than computing all-pairs shortest distances, up to a polylogarithmic factor. Finally, we present a solution for the general all-pairs shortest distance LCA problem based on computing all-pairs all LCAs.