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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/847317 |
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| author | Bingwu Zhang Xiucui Guan Chunyuan He Shuguo Wang |
| author_facet | Bingwu Zhang Xiucui Guan Chunyuan He Shuguo Wang |
| author_sort | Bingwu Zhang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-c65a357e10bd4d99859a918a2cf93f37 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c65a357e10bd4d99859a918a2cf93f372025-02-03T01:11:05ZengWileyJournal 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 |
| spellingShingle | Bingwu Zhang Xiucui Guan Chunyuan He Shuguo Wang Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance Journal of Applied Mathematics |
| title | 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_short | Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance |
| title_sort | algorithms for the shortest path improvement problems under unit hamming distance |
| url | http://dx.doi.org/10.1155/2013/847317 |
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