Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance
نویسندگان
چکیده
منابع مشابه
A Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance
A preliminary version of this article appeared in Proceedings of the 35th International Colloquium on Automata, Languages, and Programming (ICALP), Reykjavik, Iceland, July 7-11, 2008. Author’s addresses: Bernhard Haeupler, CSAIL, Massachusetts Institute of Technology, Cambridge, MA 02139, United States, [email protected]; work done while the author was a visiting student at Princeton University...
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We present an on-line algorithm for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our algorithm takes O(m) amortized time per arc, where m is the total number of arcs. For sparse graphs, this bound improves the best previous bound by a logarithmic factor and is tight to within a constant factor for a natural class of al...
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We present two online algorithms for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm takes O(m) amortized time per arc and our second algorithm takes O(n/m) amortized time per arc, where n is the number of vertices and m is the total number of arcs. For sparse graphs, our O(m) bound improves the best p...
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Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only analyzed for worst-case insertion sequences or only evaluated experimentally on random DAGs. We present the first averagecase analysis of incremental topological ...
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Let G = (V,E) be a directed acyclic graph (dag) with n = |V | and m = |E|. We say that a total ordering ≺ on vertices V is a topological ordering if for every edge (u,v) ∈ E , we have u ≺ v. In this paper, we consider the problem of maintaining a topological ordering subject to dynamic changes to the underlying graph. That is, we begin with an empty graph G =(V, / 0) consisting of n nodes. The ...
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2012
ISSN: 1549-6325,1549-6333
DOI: 10.1145/2071379.2071382