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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 847317, 8 pages
http://dx.doi.org/10.1155/2013/847317
Research Article

Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance

1Department of Mathematics and Physics, Hohai University, Changzhou 213022, China
2Department of Mathematics, Southeast University, Nanjing 210096, China

Received 1 July 2013; Accepted 19 August 2013

Academic Editor: Frank Werner

Copyright © 2013 Bingwu Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.