Smalltalk-80: the language and its implementation
Smalltalk-80: the language and its implementation
Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
OOPLSA '86 Conference proceedings on Object-oriented programming systems, languages and applications
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)
Partial order programming (extended abstract)
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Recursive star-tree parallel data structure
SIAM Journal on Computing
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
Tree structure for distributive lattices and its applications
Theoretical Computer Science
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology
ICS '97 Proceedings of the 11th international conference on Supercomputing
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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 Some Algorithms for Multiple Inheritance in Object-Oriented Programming
ECOOP '87 Proceedings of the European Conference on Object-Oriented Programming
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
All Pairs Shortest Paths in weighted directed graphs ? exact and almost exact algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
A linear-time algorithm for a special case of disjoint set union
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Reasoning with taxonomies
A Simple and Compact Algorithm for the RMQ and Its Application to the Longest Common Repeat Problem
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
A Path Cover Technique for LCAs in Dags
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
On Cartesian Trees and Range Minimum Queries
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
New common ancestor problems in trees and directed acyclic graphs
Information Processing Letters
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
Improved bounds for range mode and range median queries
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Finding heaviest H-subgraphs in real weighted graphs, with applications
ACM Transactions on Algorithms (TALG)
Exploit keyword query semantics and structure of data for effective XML keyword search
ADC '10 Proceedings of the Twenty-First Australasian Conference on Database Technologies - Volume 104
Data structures for range minimum queries in multidimensional arrays
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On space efficient two dimensional range minimum data structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Simultaneous Identification of Duplications and Lateral Gene Transfers
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Cache-oblivious index for approximate string matching
Theoretical Computer Science
Relevant answers for XML keyword search: a skyline approach
WISE'10 Proceedings of the 11th international conference on Web information systems engineering
LRM-trees: compressed indices, adaptive sorting, and compressed permutations
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
K-graphs: selecting top-k data sources for XML keyword queries
DEXA'11 Proceedings of the 22nd international conference on Database and expert systems applications - Volume Part I
Space-Efficient Preprocessing Schemes for Range Minimum Queries on Static Arrays
SIAM Journal on Computing
Theoretical and practical improvements on the RMQ-Problem, with applications to LCA and LCE
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Optimal succinctness for range minimum queries
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Finding the smallest H-Subgraph in real weighted graphs and related problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
A 7/6-approximation algorithm for the max-min connected bipartition problem on grid graphs
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
Top-K data source selection for keyword queries over multiple XML data sources
Journal of Information Science
Efficient algorithms for local ranking
Information Processing Letters
Deterministic regular expressions in linear time
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Finding cross genome patterns in annotation graphs
DILS'12 Proceedings of the 8th international conference on Data Integration in the Life Sciences
Two-dimensional range minimum queries
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Adaptive Tuple differential coding
DEXA'07 Proceedings of the 18th international conference on Database and Expert Systems Applications
All-pairs ancestor problems inweighted dags
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
A new succinct representation of RMQ-information and improvements in the enhanced suffix array
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Measuring Relatedness Between Scientific Entities in Annotation Datasets
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
Towards automatic software lineage inference
SEC'13 Proceedings of the 22nd USENIX conference on Security
Making queries tractable on big data with preprocessing: through the eyes of complexity theory
Proceedings of the VLDB Endowment
A scalable approach to computing representative lowest common ancestor in directed acyclic graphs
Theoretical Computer Science
Journal of Combinatorial Optimization
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We study the problem of finding lowest common ancestors (LCA) in trees and directed acyclic graphs (DAGs). Specifically, we extend the LCA problem to DAGs and study the LCA variants that arise in this general setting. We begin with a clear exposition of Berkman and Vishkin's simple optimal algorithm for LCA in trees. Their ideas lay the foundation for our work on LCA problems in DAGs. We present an algorithm that finds all-pairs-representative LCA in DAGs in O@?(n^2^.^6^8^8) operations, provide a transitive-closure lower bound for the all-pairs-representative-LCA problem, and develop an LCA-existence algorithm that preprocesses the DAG in transitive-closure time. We also present a suboptimal but practical O(n^3) algorithm for all-pairs-representative LCA in DAGs that uses ideas from the optimal algorithms in trees and DAGs. Our results reveal a close relationship between the LCA, all-pairs-shortest-path, and transitive-closure problems. We conclude the paper with a short experimental study of LCA algorithms in trees and DAGs. Our experiments and source code demonstrate the elegance of the preprocessing-query algorithms for LCA in trees. We show that for most trees the suboptimal @Q(nlogn)-preprocessing @Q(1)-query algorithm should be preferred, and demonstrate that our proposed O(n^3) algorithm for all-pairs-representative LCA in DAGs performs well in both low and high density DAGs.