Edge Weight Reduction Problems in Directed Acyclic Graphs

Let G be a weighted, direr.ted, acyclic graph in which each edge weight. is not a staticquantity, but can be reduced for a certain cost. In this paper we consider the problem of determining which edg('s to reduce so that the length of the longest paths is minimized and the total cost associated with the reductions does not exceed a given cost. We consider two type-s of edge reductions, linear reductions and 0/1 reductions, which model different applications. We present efficient algorithms for different classes of graphs, including trel's, series-parallel graphs, and directed ac.ydic graphs, and we show other edge reduction problems to be NP-hard.