Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
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Journal of the ACM (JACM)
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Information Processing Letters
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Theoretical Computer Science
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Information Processing Letters
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
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SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
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OOPSLA '02 Proceedings of the 17th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
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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
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Theoretical Computer Science
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ACM Transactions on Algorithms (TALG)
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Discrete Applied Mathematics
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ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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ACM Transactions on Algorithms (TALG)
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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{m3/2logn, m3/2 + n2logn}) 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(mklog2n) for general k and that it can be implemented to run in O(nlog n) time on trees, which is optimal. The algorithm also detects cycles in the input.