Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance. (26th September 2013)

• Record Type: Journal Article
• Authors: Zhang, Bingwu; Guan, Xiucui; He, Chunyuan; Wang, Shuguo
• Other Names: Werner Frank Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-09-26
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/847317
• Languages: English
• ISSNs: 1110-757X

Abstract

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.