Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
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STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
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IEEE Transactions on Computers
On competitive on-line algorithms for the dynamic priority-ordering problem
Information Processing Letters
Maintaining a topological order under edge insertions
Information Processing Letters
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SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
SIAM Journal on Computing
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Information Processing Letters
Communications of the ACM
Data Structures and Algorithms
Data Structures and Algorithms
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On-line Graph Algorithms for Incremental Compilation
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Journal of Computer and System Sciences - Special issue: STOC 2003
ACM Transactions on Algorithms (TALG)
A dynamic topological sort algorithm for directed acyclic graphs
Journal of Experimental Algorithmics (JEA)
A tight analysis of the Katriel–Bodlaender algorithm for online topological ordering
Theoretical Computer Science
Improved Dynamic Reachability Algorithms for Directed Graphs
SIAM Journal on Computing
Faster Algorithms for Incremental Topological Ordering
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A new approach to incremental topological ordering
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Journal of Computer and System Sciences
Journal of Computer and System Sciences
An O(n2.75) algorithm for online topological ordering
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Time-Dependent simple temporal networks
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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We present two online algorithms for maintaining a topological order of a directed n-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles m arc additions in O(m3/2) time. For sparse graphs (m/n = O(1)), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural locality property. Our second algorithm handles an arbitrary sequence of arc additions in O(n5/2) time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take Ω(n22√2 lg n) time by relating its performance to a generalization of the k-levels problem of combinatorial geometry. A completely different algorithm running in Θ(n2 log n) time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.