Introduction to algorithms
Shostak's Congruence Closure as Completion
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
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
Constructing rewrite-based decision procedures for embeddings and termination
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
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We propose a cooperating Knuth-Bendix completion procedure for transitive relations and equivalences and apply it as a data structure for novel dynamic strongly connected component algorithms. Benefits are separation of declarative and procedural concerns, simple generic specifications and flexible optimisation via execution strategies.