Average-case analysis of incremental topological ordering

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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Average-Case Analysis of Online Topological Ordering

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 average-case analysis of online topological orde...

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eb 2 00 8 Average - Case Analysis of Online Topological Ordering ∗

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 average-case analysis of online topological orde...

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Faster Algorithms for Incremental Topological Ordering

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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Incremental Topological Ordering and Strong Component Maintenance

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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Average-case analysis of incremental topological ordering

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