调度单元处理时间弧关断作业以最大化网络流量随时间的变化：复杂性结果
Scheduling unit processing time arc shutdown jobs to maximize network flow over time: complexity results
摘要：
研究了在容量受限的网络中，以最大化从源节点到汇聚节点的总流量为目标的弧段维护调度问题。对电弧的维护在其维护被调度的时段的持续时间内关闭电弧，使得其容量在该时段为零。一组弧被指定在规划期间进行维护，这将要求每个弧关闭一段时间。一般来说，这个问题是NP难的。在这里，我们确定了一些与实例类的复杂性相关的特征。特别是，我们讨论的情况下，有维护计划的弧集的限制;串联并行网络;平衡的能力，在这个意义上说，进入（非终端）节点的弧的总容量等于离开节点的弧的总容量;和相同的能力，所有的弧。
英文摘要：
We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NP-hard. Here we identify a number of characteristics that are relevant for the complexity of instance classes. In particular, we discuss instances with restrictions on the set of arcs that have maintenance to be scheduled; series parallel networks; capacities that are balanced, in the sense that the total capacity of arcs entering a (non-terminal) node equals the total capacity of arcs leaving the node; and identical capacities on all arcs.
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