An improved average distance heuristic for Steiner problem in networks

Pao Yue-kong Library Electronic Theses Database

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:
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.

Files in this item

Files Size Format
b12313257.pdf 3.240Mb PDF
Copyright Undertaking
As a bona fide Library user, I declare that:
  1. I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
  2. I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
  3. I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.
By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.


Quick Search


More Information