Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

In a shortest path improvement problem under unit Hamming distance (denoted by SPIUH), an edge weighted graph with a set of source-terminal pairs is given; we need to modify the lengths of edges by a minimum cost under unit Hamming distance such that the modified distances of the shortest paths are...

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Main Authors: Bingwu Zhang, Xiucui Guan, Chunyuan He, Shuguo Wang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/847317
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spelling doaj-c65a357e10bd4d99859a918a2cf93f372020-11-25T00:15:23ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/847317847317Algorithms for the Shortest Path Improvement Problems under Unit Hamming DistanceBingwu Zhang0Xiucui Guan1Chunyuan He2Shuguo Wang3Department of Mathematics and Physics, Hohai University, Changzhou 213022, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaDepartment of Mathematics and Physics, Hohai University, Changzhou 213022, ChinaDepartment of Mathematics and Physics, Hohai University, Changzhou 213022, ChinaIn a shortest path improvement problem under unit Hamming distance (denoted by SPIUH), an edge weighted graph with a set of source-terminal pairs is given; we need to modify the lengths of edges by a minimum cost under unit Hamming distance such that the modified distances of the shortest paths are upper bounded by given values. The SPIUH problem on arborescent network is formulated as a 0-1 integer programming model. Some strongly polynomial time algorithms are designed for the problems on some special arborescent networks. Firstly, two greedy algorithms are proposed for problems on chain networks and special star-tree networks, respectively. Secondly, a strongly polynomial time algorithm is presented for the problem with a single source and constrained paths. Finally, a heuristic algorithm and its computational experiments are given for the SPIUH problem on general graphs.http://dx.doi.org/10.1155/2013/847317
collection DOAJ
language English
format Article
sources DOAJ
author Bingwu Zhang
Xiucui Guan
Chunyuan He
Shuguo Wang
spellingShingle Bingwu Zhang
Xiucui Guan
Chunyuan He
Shuguo Wang
Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
Journal of Applied Mathematics
author_facet Bingwu Zhang
Xiucui Guan
Chunyuan He
Shuguo Wang
author_sort Bingwu Zhang
title Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
title_short Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
title_full Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
title_fullStr Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
title_full_unstemmed Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
title_sort algorithms for the shortest path improvement problems under unit hamming distance
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description In a shortest path improvement problem under unit Hamming distance (denoted by SPIUH), an edge weighted graph with a set of source-terminal pairs is given; we need to modify the lengths of edges by a minimum cost under unit Hamming distance such that the modified distances of the shortest paths are upper bounded by given values. The SPIUH problem on arborescent network is formulated as a 0-1 integer programming model. Some strongly polynomial time algorithms are designed for the problems on some special arborescent networks. Firstly, two greedy algorithms are proposed for problems on chain networks and special star-tree networks, respectively. Secondly, a strongly polynomial time algorithm is presented for the problem with a single source and constrained paths. Finally, a heuristic algorithm and its computational experiments are given for the SPIUH problem on general graphs.
url http://dx.doi.org/10.1155/2013/847317
work_keys_str_mv AT bingwuzhang algorithmsfortheshortestpathimprovementproblemsunderunithammingdistance
AT xiucuiguan algorithmsfortheshortestpathimprovementproblemsunderunithammingdistance
AT chunyuanhe algorithmsfortheshortestpathimprovementproblemsunderunithammingdistance
AT shuguowang algorithmsfortheshortestpathimprovementproblemsunderunithammingdistance
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