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- W1569442745 abstract "A dynamic network consists of a directed graph with capacities, costs and integral transit times on the arcs. In the minimum cost dynamic flow problem MCDFP, the goal is to compute for a given dynamic network with source s, sink t and two integers υ and T, a feasible dynamic flow from s to t of value υ, obeying the time bound T, and having minimum total cost. MCDFP contains as subproblems the minimum cost maximum dynamic flow problem (fix υ to the maximum amount of flow that can be sent from s to t within time T), and the minimum cost quickest flow problem (fix T to the minimum time needed for sending υ units of flow from s to t). We first prove that both subproblems are NP-hard even on two-terminal series-parallel graphs with unit capacities. As main result, we formulate a greedy algorithm for MCDFP and provide a full characterization via forbidden subgraphs of the class G of graphs, for which this greedy algorithm always yields an optimum solution (for arbitrary choices of problem parameters). G is a subclass of the class of two-terminal series-parallel graphs. It is shown that the greedy algorithm solves MCDFP restricted to graphs in G in polynomial time." @default.
- W1569442745 created "2016-06-24" @default.
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- W1569442745 date "1995-01-01" @default.
- W1569442745 modified "2023-09-23" @default.
- W1569442745 title "Minimum cost dynamic flows: The series-parallel case" @default.
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- W1569442745 doi "https://doi.org/10.1007/3-540-59408-6_62" @default.
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