A Labeling Algorithm for the Earliest and Latest Time-Varying Maximum Flow Problems

Jianming Zhu, D. Sha
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Abstract

The time-varying maximum flow problem is to find the maximum flow in a time-varying network. A time-varying network is the network which the transit time and the capacity of an arc are functions of the departure time at the beginning node of an arc. The earliest (or the latest) maximum flow is the maximum flow could be sent from the source node to the sink node in the time-varying network within the given time duration with the earliest (or the latest) arrival time. We assume that the transit time and the capacity of an arc are positive integers, and waiting at any node is prohibited except the source node. The problem is known to be NP-complete. A labeling algorithms is proposed for solving problems in pseudo polynomial time.
最早和最迟时变最大流问题的标记算法
时变最大流量问题是求时变网络中的最大流量。时变网络是弧的穿越时间和容量是弧起始节点出发时间的函数的网络。最早(或最晚)最大流量是指时变网络中在给定时间段内,到达时间最早(或最晚)的源节点向汇聚节点发送的最大流量。我们假设电弧的通过时间和容量为正整数,并且在除源节点外的任何节点禁止等待。已知这个问题是np完全的。提出了一种求解伪多项式时间问题的标记算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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