Journal of Applied Mathematics

Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

Bingwu Zhang, Xiucui Guan, Chunyuan He, and Shuguo Wang

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 847317, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808140

Digital Object Identifier
doi:10.1155/2013/847317

Mathematical Reviews number (MathSciNet)
MR3108927

Zentralblatt MATH identifier
06950904

Citation

Zhang, Bingwu; Guan, Xiucui; He, Chunyuan; Wang, Shuguo. Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance. J. Appl. Math. 2013 (2013), Article ID 847317, 8 pages. doi:10.1155/2013/847317. https://projecteuclid.org/euclid.jam/1394808140


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