The KIPS Transactions:PartA (정보처리학회논문지A)

Korea Information Processing Society (한국정보처리학회)
권호 표지
DOI QR코드

DOI QR Code

A Proposal of Heuristic Using Zigzag Steiner Point Locating Strategy for GOSST Problem

GOSST 문제 해결을 위한 지그재그 스타이너 포인트 배치 방법을 이용한 휴리스틱의 제안

  • Published : 2007.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

We propose more enhanced heuristic for the GOSST(Grade of Services Steiner Minimum Tree) problem in this paper. GOSST problem is a variation of Steiner Tree problem and to find a network topology satisfying the G-Condition with minimum network construction cost. GOSST problem is known as one of NP-Hard or NP-Complete problems. In previous our research, we proposed a heuristic employing Direct Steiner Point Locating strategy with Distance Preferring MST building strategy. In this paper, we propose new Steiner point locating strategy, Zigzag Steiner point Locating strategy. Through the results of out experiments, we can assert this strategy is better than our previous works. The Distance Zigzag GOSST method which hires the Distance Preferring MST building strategy and Zigzag Steiner point Locating strategy defrays the least network construction cost and brings 31.5% cost saving by comparison to G-MST, the experimental control and 2.2% enhancement by comparison to the Distance Direct GOSST method, the best GOSST method in our previous research.

본 논문에서 GOSST(Grade of Services Steiner Minimum Tree) 문제에 대한 개선된 휴리스틱을 제안한다. GOSST 문제는 스타이너 포인트 문제의 한 변형으로 G-Condition을 만족하는 최소비용의 네트워크 구성을 찾는 문제이며, NP-Hard 혹은 NP-Complete 문제로 알려져 있다. 이 문제에 대한 이전의 연구에서 우리는 거리 우선 최소 신장 트리 생성방법과 직접 스타이너 포인트 배치 방법을 결합한 휴리스틱을 제안했었다. 본 논문에서는 스타이너 포인트 배치 방법으로 지그재그 스타이너 포인트 배치방법을 새롭게 제안한다. 이 방법과 거리우선 최소 신장 트리 생성 방법을 결합한 거리 지그재그 GOSST 휴리스틱은 컨트롤인 G-MST에 비해 31.5%의 네트워크 구축 비용의 절감을 얻었고 이전의 가장 좋은 GOSST 휴리스틱인 거리 직접 GOSST 휴리스틱에 비해 2.2%의 비용 개선을 보였다.

Keywords

References

  1. D.Z, Du and F.K. Hwang, 'An Approach for Providing Lower Bounds; Solution of Gilbert-Pollak Conjecture on Steiner Ratio', Proceedings of IEEE 31sy FOCS, pp.76-85, 1990 https://doi.org/10.1109/FSCS.1990.89526
  2. G.L. Xue, G.H. Lin and D.Z. Du, 'Grade of Service Steiner Minimum Trees in Euclidean Plane', Algorithmica, Vol.31, pp.479-500, 2001 https://doi.org/10.1007/s00453-001-0050-6
  3. J. Kim and I. Kim, 'Approximation Ratio 2 for the Minimum Number of Steiner Points', Journal of KISS, pp.387-396, 2003
  4. J. Kim, M. Cardei, I. Cardei and X. Jia, 'A Polynomial Time Approximation Scheme for the Grade of Service Steiner Minimum Tree Problem', Algorithrnica, Vol.42, pp.109-120, 2005
  5. S. Arora, 'Polynomial-Time Approximation Schemes for Euclidean TSP and Other Geometric Problems', Proceeding of 37th IEEE Symposium on Foundations of Computer Science, pp.2-12, 1996 https://doi.org/10.1109/SFCS.1996.548458
  6. T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms, 2nd Ed., MIT Press, 2001
  7. E.J. Cockayne and D.E. Hewgrill, 'Exact Computation of Steiner Minimal Trees in the Plane', Information Processing Letters, Vol.22, pp.151-156, 1986 https://doi.org/10.1016/0020-0190(86)90062-1
  8. E.J. Cockayne and D.E. Hewgrill, 'Improved Computation of Plane Steiner Minimal Tree', Algorithrnica, Vol.7, pp.219-229, 1992 https://doi.org/10.1007/BF01758759
  9. F.K. Hwang, 'A Primer of the Euclidean Steiner problem', Annals of Operations Research, Vol.33, pp.73-84, 1991 https://doi.org/10.1007/BF02061658
  10. F.K Hwang, D.S. Richards and P. Wmter, 'The Steiner Tree Problem', Annals of Discrete Mathematics, Vol.53, North-Holland, 1992
  11. M.J. Smith and B. Toppur, 'Euclidean Steiner Minimal Trees, Minimum Energy Configurations and the Embedding Problem of Weighted Graph in E3', Discrete Applied Mathematics, Vol.71, pp.187-215, 1997 https://doi.org/10.1016/S0166-218X(96)00064-9
  12. P. Winter, 'An Algorithm for the Steiner Problem in the Euclidean Plane', Networks, Vol.15, pp.323-345, 1985 https://doi.org/10.1002/net.3230150305
  13. I. Kim, C. Kim and S.H. Hosseini, 'A Heuristic Using GOSST with 2 Connecting Strategies for Minimum Construction Cost of Network', International Journal of Computer Science and Network Security, Vol.6, No.12, pp.60-72, 2006
  14. I. Kim and C. Kim, 'An Enhanced Heuristic Using Direct Steiner Point Locating and Distance Preferring MST Building Strategy for GOSST Problem', International Journal of Computer Science and Network Security, Vol.7, No.2, pp.164-175, 2007
  15. A. Balakrishnan, T.L. Nagnanti and P. Mirchandani, 'Modeling and Heuristic Worst Case Performance Analysis of the Two Level Network Design Problem', Management Science, Vol.40, pp.846-867, 1994 https://doi.org/10.1287/mnsc.40.7.846
  16. C. Duin and A. Volgenant, 'The Multi-weighted Steiner Tree Problem', Annals of Operations Research, Vol.33, pp.451-469, 1991 https://doi.org/10.1007/BF02071982
  17. G.H. Lin and G.L. Xue , 'Steiner Tree Problem with Minimum Number of Steiner Points and Bounded Edge-length', Information Processing Letters, pp.53-57, 1999 https://doi.org/10.1016/S0020-0190(98)00201-4
  18. J.R Current, C.S. Revelle and J.L. Cohon, 'The Hierarchical Network Design Problem', European Journal of Operational Research, Vol.27, pp.57-66, 1986 https://doi.org/10.1016/S0377-2217(86)80007-8
  19. P. Mirchandani, 'The Multi-tier Tree Problem', INFORMS Journal on Computing, Vol.8, pp.202~218, 1996 https://doi.org/10.1287/ijoc.8.3.202
  20. P. Winter and M. Zachariasen, 'Large Euclidean Steiner Minimum Trees: An Improved Exact Algorithm', Networks, Vol.30, pp.149-166, 1998