Upgrading Vertices In Trees, Series-Parallel Digraphs And General Series-Parallel Digraphs To Bound Path Length+

We consider trees, series-parallel digraphs, and general series-parallel digraphs that have vertex weights and delays. The length/delay of a path is the sum of the delays on the path. We show that minimal weight vertex subsets X such that the length of the longest path is bounded by a given value δ when all vertices in X are upgraded to have delay 0 can be found in pseudo polynomial time. In case all delays are unit or all weights are unit, our algorithms have a quadratic complexity. For the case of trees with unit weights and unit delays, we develop a linear time algorithm.