Average Longest Path and Maximum Cost Network Flows with Multiple-Criteria Weights

Q2 Mathematics Electronic Notes in Discrete Mathematics Pub Date : 2018-08-01 DOI:10.1016/j.endm.2018.07.024

Jeremy D. Jordan, Jeffery D. Weir

引用次数: 2

Abstract

Multiple criteria decision analysis methods are incorporated into network flow problems as the arc weight. Each individual arc in the network consequently has a value or utility between 0 and 1, and the objective is thus to find the path with longest average value or maximum average cost flow. These problems are NP-hard for general graphs. For directed acyclic graphs (DAG), we develop a dynamic programming based algorithm to solve the average longest path problem in O(nm) and a heuristic to approximate the average longest path problem in O(m). These methods are then used successively to approximate the average maximum cost flow.

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具有多准则权值的平均最长路径和最大代价网络流

将多准则决策分析方法作为电弧权值纳入网络流问题。因此，网络中的每个弧的值或效用在0到1之间，目标是找到具有最长平均值或最大平均成本流的路径。这些问题对于一般图来说是np困难的。对于有向无环图(DAG)，我们开发了一种基于动态规划的算法来解决O(nm)内的平均最长路径问题和一种启发式算法来近似O(m)内的平均最长路径问题。然后依次使用这些方法来近似平均最大成本流。

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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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

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期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.

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