Introduction to algorithms
On competitive on-line algorithms for the dynamic priority-ordering problem
Information Processing Letters
Maintaining a topological order under edge insertions
Information Processing Letters
Incremental evaluation of computational circuits
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On-line Graph Algorithms for Incremental Compilation
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Uniform hashing in constant time and linear space
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
A new approach to incremental topological ordering
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Average-case analysis of incremental topological ordering
Discrete Applied Mathematics
Average-case analysis of online topological ordering
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A batch algorithm for maintaining a topological order
ACSC '10 Proceedings of the Thirty-Third Australasian Conferenc on Computer Science - Volume 102
Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance
ACM Transactions on Algorithms (TALG)
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We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in ${\cal O}(n^{2.75})$ time, independent of the number of edges m inserted. For dense DAGs, this is an improvement over the previous best result of ${\cal O}(\min\{m^{\frac{3}{2}} \log{n}, m^{\frac{3}{2}} + n^2 \log{n}\})$ by Katriel and Bodlaender. We also provide an empirical comparison of our algorithm with other algorithms for online topological sorting