An improved average distance heuristic for Steiner problem in networks

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An improved average distance heuristic for Steiner problem in networks

 

Author: Tang, Chun-ming
Title: An improved average distance heuristic for Steiner problem in networks
Degree: M.Sc.
Year: 1996
Subject: Steiner systems
Hong Kong Polytechnic University -- Dissertations
Department: Multi-disciplinary Studies
Pages: vi, 106 p. : ill. ; 31 cm
Language: English
InnoPac Record: http://library.polyu.edu.hk/record=b1231325
URI: http://theses.lib.polyu.edu.hk/handle/200/4810
Abstract: The average distance heuristic (ADH) was first given by Rayward-Smith (1983). Rayward-Smith and Clare (1986) later modified the ADH and showed that the revised version gave better Steiner trees than the shortest path heuristic (SPH). Winter and MacGregor Smith (1992) showed by running experiments that two repetitive versions of the shortest path heuristic. SPH-V and SPH-ZZ, outperformed all other single-pass path-distance heuristics including ADH and SPH. In this project the heuristic ADH32 has been developed by modifying the heuristic function of the original average distance heuristic (ADH) given by Rayward-Smith and Clare (1986). The main modification is to consider the average distance of a vertex to the 3 or more closest trees instead of two at each iteration. The performance of this heuristic and its double-pass version ADH32S have been compared with ADH as well as the repetitive shortest path heuristics SPH-V and SPH-ZZ which were shown to give better Steiner trees than other path-distance heuristics by Winter and MacGregor Smith (1992). Steiner trees computed by six heuristics (SPH, SPH-V, SPH-ZZ, ADH, ADH32 and ADH32S) for 400 random networks and 400 Euclidean networks were compared and in the experiment reduction tests had been employed to simplify the networks whenever possible. Experimental results showed that ADH32 on average gave better solutions than the other two single-pass heuristics ADH and SPH. The performance of ADH32S was second only to SPH-ZZ in the random networks and came out to be the best performer in the Euclidean networks. Both ADH32 and ADH32S have been shown to have a worst-case time complexity O(|Z|‧|V|3) where |Z| is the number of terminals and |V| is the number of vertices. The cost of the Steiner trees given by ADH32 and ADH32S are both bounded above by 2 - 2 / |Z| times the cost of the optimal solution.

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