Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
Finding paths and deleting edges in directed acyclic graphs
Information Processing Letters
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Path-based depth-first search for strong and biconnected components
Information Processing Letters
Nearest common ancestors: a survey and a new distributed algorithm
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Introduction to Algorithms
A faster and simpler fully dynamic transitive closure
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Dynamic Reachability Algorithms for Directed Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
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
Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
An Experimental Study of Dynamic Algorithms for Transitive Closure
Journal of Experimental Algorithmics (JEA)
Incremental maintenance of shortest distance and transitive closure in first-order logic and SQL
ACM Transactions on Database Systems (TODS)
Fast computing reachability labelings for large graphs with high compression rate
EDBT '08 Proceedings of the 11th international conference on Extending database technology: Advances in database technology
An experimental study of algorithms for fully dynamic transitive closure
Journal of Experimental Algorithmics (JEA)
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Average-case analysis of incremental topological ordering
Discrete Applied Mathematics
Dynamic plane transitive closure
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Average-case analysis of online topological ordering
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Proceedings of the forty-second ACM symposium on Theory of computing
Connectivity oracles for failure prone graphs
Proceedings of the forty-second ACM symposium on Theory of computing
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
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
GRAIL: scalable reachability index for large graphs
Proceedings of the VLDB Endowment
Linear time analysis of properties of conflict-free and general Petri nets
Theoretical Computer Science
Journal of Network and Systems Management
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
An experimental study of algorithms for fully dynamic transitive closure
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Dynamic complexity theory revisited
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
I/O cost minimization: reachability queries processing over massive graphs
Proceedings of the 15th International Conference on Extending Database Technology
Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication
ACM Transactions on Algorithms (TALG)
Connectivity games over dynamic networks
Theoretical Computer Science
Computing weight constraint reachability in large networks
The VLDB Journal — The International Journal on Very Large Data Bases
Hi-index | 0.00 |
We obtain a new fully dynamic algorithm for the reachability problem in directed graphs. Our algorithm has an amortized update time of O(m+n log n) and a worst-case query time of O(n), where m is the current number of edges in the graph, and n is the number of vertices in the graph. Each update operation either inserts a set of edges that touch the same vertex, or deletes an arbitrary set of edges. The algorithm is deterministic and uses fairly simple data structures. This is the first algorithm that breaks the O(n2) update barrier for all graphs with o(n2) edges.One of the ingredients used by this new algorithm may be interesting in its own right. It is a new dynamic algorithm for strong connectivity in directed graphs with an interesting persistency property. Each insert operation creates a new version of the graph. A delete operation deletes edges from emphall versions. Strong connectivity queries can be made on each version of the graph. The algorithm handles each update in O(mα(m,n)) amortized time, and each query in O(1) time, where α(m,n) is a functional inverse of Ackermann's function appearing in the analysis of the union-find data structure. Note that the update time of O(mα(m,n)), in case of a delete operation, is the time needed for updating all versions of the graph.