critical path problem

(classic problem)

Definition: Find the longest path from any source to any sinks in a directed acyclic graph which has weights, or numeric values, on vertices.

Note: This can be solved with a variant of the DAG shortest paths algorithm by assigning an initial distance of negative infinity (-∞), updating the distance and predecessor if dist(v) + weight(u) > dist(u), and recording the greatest distance found so far.

Author: PEB

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Entry modified 19 April 2004.
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Cite this as:
Paul E. Black, "critical path problem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 19 April 2004. (accessed TODAY) Available from: