Amortized efficiency of a path retrieval data structure
Theoretical Computer Science
Finding paths and deleting edges in directed acyclic graphs
Information Processing Letters
Maintenance of transitive closures and transitive reductions of graphs
Proceedings of the International Workshop WG '87 on Graph-theoretic concepts in computer science
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Fast rectangular matrix multiplication and applications
Journal of Complexity
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A fully dynamic algorithm for maintaining the transitive closure
Journal of Computer and System Sciences - STOC 1999
Fully dynamic biconnectivity and transitive closure
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Dynamic Transitive Closure via Dynamic Matrix Inverse (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
An experimental study of algorithms for fully dynamic transitive closure
Journal of Experimental Algorithmics (JEA)
Consensus Genetic Maps as Median Orders from Inconsistent Sources
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Towards polynomial lower bounds for dynamic problems
Proceedings of the forty-second ACM symposium on Theory of computing
New data structures for subgraph connectivity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Algorithms and theory of computation handbook
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
Algorithms and constraint programming
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Reachability in graph timelines
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Improved Deterministic Algorithms for Decremental Reachability and Strongly Connected Components
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Simple deterministic algorithms for fully dynamic maximal matching
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present an algorithm for directed acyclic graphs that breaks through the O(n2) barrier on the single-operation complexity of fully dynamic transitive closure, where n is the number of edges in the graph. We can answer queries in O(nε) worst-case time and perform updates in O(nω(1,ε,1)−ε+n1+ε) worst-case time, for any ε∈[0,1], where ω(1,ε,1) is the exponent of the multiplication of an n × nε matrix by an nε × n matrix. The current best bounds on ω(1,ε,1) imply an O(n0.575) query time and an O(n1.575) update time in the worst case. Our subquadratic algorithm is randomized, and has one-sided error. As an application of this result, we show how to solve single-source reachability in O(n1.575) time per update and constant time per query.