Journal of the Korea Society of Computer and Information (한국컴퓨터정보학회논문지)

Korean Society of Computer Information (한국컴퓨터정보학회)
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Efficient Construction of Euclidean Minimum Spanning Tree Using Partial Polynomial-Time Approximation Scheme in Unequality Node Distribution

비 균등 노드 분포환경에서 부분 PTAS를 이용한 효과적인 유클리드 최소신장트리 생성

  • 김인범 (김포대학교 인터넷정보과) ;
  • 김수인 (김포대학교 항공전기전자과)
  • Received : 2014.05.19
  • Accepted : 2014.06.14
  • Published : 2014.06.30
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Abstract

Employing PTAS to building minimum spanning tree for a large number of equal distribution input terminal nodes can be a effective way in execution time. But applying PTAS to building minimum spanning tree for tremendous unequal distribution node may lead to performance degradation. In this paper, a partial PTAS reflecting the scheme into specific node dense area is presented. In the environment where 90% of 50,000 input terminal nodes stand close together in specific area, approximate minimum spanning tree by our proposed scheme can show about 88.49% execution time less and 0.86%tree length less than by existing PTAS, and about 87.57%execution time less and 1.18% tree length more than by Prim's naive scheme. Therefore our scheme can go well to many useful applications where a multitude of nodes gathered around specific area should be connected efficiently as soon as possible.

균등하게 분포된 많은 입력노드들을 최소비용으로 연결하는 최소신장트리 생성문제에 PTAS를 사용하면 실행시간에 있어서 효과적으로 결과를 얻을 수 있다. 그러나 비 균등 분포의 경우에는 PTAS 적용이 오히려 성능을 저하시킬 수 있다. 본 논문에서는 특정 영역에 노드들이 밀집된 경우 해당 영역에만 PTAS를 적용한 부분 PTAS를 제안한다. 이 방법은 50,000개 입력노드들의 90%가 특정 영역에 밀집된 환경에서 기존의 PTAS 방식에 비해서 생성시간은88.49%, 트리길이는 0.86%감소를 보였고, Prim의 Naive 최소신장트리 생성방법에 비해서 생성시간은 87.57% 감소, 트리길이는 1.18% 증가를 보였다. 따라서 본 연구의 제안방법은 많은 노드들이 특정영역에 밀집된 환경에서 이 노드들을 빠른 시간 내에 연결해야 하는 응용 등에 잘 적용될 수 있을 것이다.

Keywords

References

  1. T.H. Cormen, C.E Leiserson, R.L. Rivest and C. Stein, "Introduction to Algorithms," 2nd Ed., The MIT Press, pp.561-579, 2001
  2. PTAS(Polynomial Time Approximation Scheme), http://en.wikipedia.org/wiki/Polynomial-time_a pproximation_scheme, May, 2014.
  3. F.Grandoni and T.RothvoB, "Pricing on paths: a PTAS for the highway problem," SODA '11 Proceedings of the twenty-second annual symposium on Discrete Algorithms, pp. 675-684, 2011
  4. Z. Cao and X. Yang, "A PTAS for parallel batch scheduling with rejection and dynamic job arrivals", Journal of Theoretical Computer Science archive, Vol.410, No.27-29, pp. 2732-2745. June, 2009 https://doi.org/10.1016/j.tcs.2009.04.006
  5. T. Erlebach and E. Leeuwen, "PTAS for weighted set cover on unit squares," APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques, pp.166-177, 2010
  6. Z.Zhang, X.Gao, W.Wu and D.Du, "A PTAS for minimum connected dominating set in 3-dimensional Wireless sensor networks," Journal of Global Optimization archive, Vol.45 No.3, pp.451-458, November 2009
  7. J. Kim, "Interconnection Problem among the Dense Areas of Nodes in Sensor Networks," Journal of the Institute of Electronics Engineers of Korea TC, Vol.48, No.2, pp.6-13, 2011
  8. I. Kim, "Efficient Construction of Large Scale Grade of Services Steiner Tree Using Space Locality and Polynomial-Time Approximation Scheme," Journal of the Korea Society of Computer and Information, Vol.16, No.11, pp.153-161, 2011 https://doi.org/10.9708/jksci.2011.16.11.153