Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
On competitive on-line algorithms for the dynamic priority-ordering problem
Information Processing Letters
On the computational complexity of dynamic graph problems
Theoretical Computer Science
Maintaining a topological order under edge insertions
Information Processing Letters
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
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
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Maintaining Longest Paths Incrementally
Constraints
A dynamic topological sort algorithm for directed acyclic graphs
Journal of Experimental Algorithmics (JEA)
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
An O(n2.75) algorithm for online topological ordering
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Reallocation problems in scheduling
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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It is shown that the problem of maintaining the topological order of the nodes of a directed acyclic graph while inserting m edges can be solved in O(min{m3/2 log n m3/3 + n2 log n}) time, an improvement over the best known result of O(mn). In addition, we analyze the complexity of the same algorithm with respect to the treewidth k of the underlying undirected graph. We show that the algorithm runs in time O(mk log2 n) for general k and that it can be implemented to run in O(n log n) time on trees, which is optimal. If the input contains cycles, the algorithm detects this.