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Approximation ratio 2 for the Minimum Number of Steiner Points  

김준모 (한국정보보호진흥원)
김인범 (김포대학 컴퓨터계열)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.30, no.7_8, 2003 , pp. 387-396 More about this Journal
Abstract
This paper provides an approximation algorithm for STP-MSP(Steiner Tree Problem with minimum number of Steiner Points).Because it seems to be impossible to have a PTAS(Polynomial Time Approximation Schemes), which gives the near optimal solutions, for the problem, the algorithm of this paper is an alternative that has the approximation ratio 2 with $n^{O(1)}$ run time. The importance of this paper is the potential to solve other related unsolved problems. The idea of this paper is to distribute the error allowance over the problem instance so that we may reduce the run time to polynomial bound out of infinitely many cases. There are earlier works[1,2] that show the approximations that have practical run times with the ratio of bigger than 2, but this paper shows the existence of a poly time approximation algorithm with the ratio 2.
Keywords
Approximation algorithm; Approximation ratio; Error allowance; polynomial bound; Run Time; Problem instance; Dynamic Program; STP-MSP(Steiner Tree Problem with Minimum Number of Steine Points); PTAS(Polynomial Time Approximation Schemes);
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