Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Approximation ratio 2 for the Minimum Number of Steiner Points

최소 개수의 스타이너 포인트를 위한 근사 비율 2

  • Published : 2003.08.01
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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.

본 논문은 STP-MSP을 위한 근사 알고리즘을 제안한다. 이 문제에 대해 근접한 최적 해법을 제공하는 PTAS를 가지는 것이 불가능하기 때문에, 본 논문의 연구는 $n^{O(1)}$의 실행 시간과 근사 비율 2를 가지는 하나의 대안을 제시한다. 본 연구의 중요성은 관련된 다른 미해결문제에 대하여 해결 가능성을 제시하는 것이다. 본 논문의 주요 제안내용은 문제 인스턴스에게 허용오차를 배분하는 것이다. 이로 인해 우리는 무한적 경우에서 다항적 범위로 실행시간을 줄일 수 있다. 관련연구[1,2]가 근사 비율이 2보다 크지만 보다 현실적인 실행시간을 갖는 근사 알고리즘들을 제시한 것이라면, 본 연구는 근사 비율이 2인 근사 알고리즘의 존재를 밝힌 것이다.

Keywords

References

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