Parallel algorithms for vehicle routing problems

K. J. Madhu, Sanjeev Saxena
{"title":"Parallel algorithms for vehicle routing problems","authors":"K. J. Madhu, Sanjeev Saxena","doi":"10.1109/HIPC.1998.737986","DOIUrl":null,"url":null,"abstract":"In a complete directed weighted graph there are jobs located at nodes of the graph. Job i has an associated processing time or handling time h/sub i/, and the job must start within a prespecified time window [r/sub i/, d/sub i/]. A vehicle can move on the arcs of the graph, at unit speed and that has to execute the jobs within their respective time windows. We consider three different problems on the CREW PRAM. (1) Find the minimum cost routes between all pairs of nodes in a network. We give an O(log/sup 3/ n) time algorithm with n/sup 4//log/sup 2/ n processors. (2) Services all locations in minimum time. The general problem is NP-complete but O(n/sup 2/) time algorithms are known for a special case; for this case we obtain an O(log/sup 3/ n) time parallel algorithm using n/sup 4//log/sup 2/ n processors and a linear time optimal parallel algorithm. (3) Minimize the sum of waiting times at all locations. The general problem is NP-complete but O(n/sup 2/) time algorithm are known for a special case; for this case, we obtain an O(log/sup 2/ n) time algorithm with n/sup 3//log n processors and also a linear time optimal parallel algorithm.","PeriodicalId":175528,"journal":{"name":"Proceedings. Fifth International Conference on High Performance Computing (Cat. No. 98EX238)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. Fifth International Conference on High Performance Computing (Cat. No. 98EX238)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/HIPC.1998.737986","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4

Abstract

In a complete directed weighted graph there are jobs located at nodes of the graph. Job i has an associated processing time or handling time h/sub i/, and the job must start within a prespecified time window [r/sub i/, d/sub i/]. A vehicle can move on the arcs of the graph, at unit speed and that has to execute the jobs within their respective time windows. We consider three different problems on the CREW PRAM. (1) Find the minimum cost routes between all pairs of nodes in a network. We give an O(log/sup 3/ n) time algorithm with n/sup 4//log/sup 2/ n processors. (2) Services all locations in minimum time. The general problem is NP-complete but O(n/sup 2/) time algorithms are known for a special case; for this case we obtain an O(log/sup 3/ n) time parallel algorithm using n/sup 4//log/sup 2/ n processors and a linear time optimal parallel algorithm. (3) Minimize the sum of waiting times at all locations. The general problem is NP-complete but O(n/sup 2/) time algorithm are known for a special case; for this case, we obtain an O(log/sup 2/ n) time algorithm with n/sup 3//log n processors and also a linear time optimal parallel algorithm.
车辆路径问题的并行算法
在完全有向加权图中,作业位于图的节点上。作业i具有关联的处理时间或处理时间h/sub i/,并且作业必须在预先指定的时间窗口[r/sub i/, d/sub i/]内启动。车辆可以在图形的弧线上以单位速度移动,并且必须在各自的时间窗口内执行作业。我们考虑了CREW婴儿车的三个不同问题。(1)找出网络中所有节点对之间的最小开销路由。我们给出了一个O(log/sup 3/ n)时间算法,n/sup 4//log/sup 2/ n个处理器。(2)在最短时间内服务所有地点。一般问题是np完全的,但O(n/sup 2/)时间算法是已知的特殊情况;对于这种情况,我们使用n/sup 4//log/sup 2/ n个处理器和线性时间最优并行算法获得了O(log/sup 3/ n)时间并行算法。(3)尽量减少所有地点的等待时间总和。一般问题是np完全的,但O(n/sup 2/)时间算法是已知的特殊情况;对于这种情况,我们得到了一个使用n/sup 3//log n个处理器的O(log/sup 2/ n)时间算法和一个线性时间最优并行算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信