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
A fully dynamic algorithm for maintaining the transitive closure
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Path-based depth-first search for strong and biconnected components
Information Processing Letters
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Introduction to Algorithms
Improved Dynamic Reachability Algorithms for Directed Graphs
FOCS '02 Proceedings of the 43rd 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)
A fully dynamic reachability algorithm for directed graphs with an almost linear update time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Incremental maintenance of shortest distance and transitive closure in first-order logic and SQL
ACM Transactions on Database Systems (TODS)
Bounded-leg distance and reachability oracles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
Dynamic plane transitive closure
ESA'07 Proceedings of the 15th annual European conference on Algorithms
PHALANX: parallel checking of expressive heap assertions
Proceedings of the 2010 international symposium on Memory management
An experimental study of algorithms for fully dynamic transitive closure
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Banshee: a scalable constraint-based analysis toolkit
SAS'05 Proceedings of the 12th international conference on Static Analysis
Path selection in user-controlled circuit-switched optical networks
Optical Switching and Networking
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We obtain a new fully dynamic algorithm for maintaining the transitive closure of a directed graph. Our algorithm maintains the transitive closure matrix in a total running time of O(mn+ (ins + del)·n2), where ins (del) is thenumber of insert (delete) operations performed. Here n is the number of vertices in the graph and m is the initial number of edges in the graph. Obviously, reachability queries canbe answered in constant time. The space required by the algorithm is O(n2). Our algorithm can also support path queries. If v is reachable from u, the algorithm can produce a path from u to v in time proportional to the length of the path. The best previously known algorithm for the problem is due to Demetrescu and Italiano [3]. Their algorithm has total running time of O(n3 + (ins + del).n2). The query time is also constant. We also present an algorithm for directed acyclic graphs (DAGs) with a total running time of O(mn + ins.n2 + del). Our algorithms are obtained by combining somenew ideas with techniques of Italiano [7], King [8], King and Thorup [10] and Frigioni et al. [4]. We also note that ouralgorithms are extremely simple and can be easily implemented.