The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

A Study on the G-Node and Disconnected Edges to Improve the Global and Local Locating Heuristic for GOSST Problem

GOSST 문제에 대한 전역적 배치와 지역적 배치 휴리스틱의 개선을 위한 G-Node와 단절에 관한 연구

  • Published : 2007.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper is on the enhancement of our heuristics for GOSST problem that could apply to the design of communication networks offering graduated services. This problem hewn as one of NP-Hard problems finds a network topology meeting the G-Condition with minimum construction cost. In our prior research, we proposed two heuristics. We suggest methods of selecting G-Node and disconnections for Global or Local locating heuristic in this research. The ameliorated Local locating heuristic retrenches 17% more network construction cost saving ratio and the reformed Global locating heuristic does 14% more than our primitives.

GOSST 문제에 대한 이전 휴리스틱의 성능 개선을 위한 새로운 제안이 본 논문에서 제시된다. 이 문제는 다양한 등급의 서비스를 제공할 수 있는 통신 네트워크의 설계 등에 적용될 수 있다. GOSST 문제는 G-Condition을 만족하는 최소 구축비용의 네트워크를 찾는 것으로 NP-HARD 문제에 포함된다. 우리는 이전의 연구에서 이 문제와 관련된 두개의 휴리스틱을 발표하였다. 본 연구에서는 스타이너 트리 생성 시 이용되는 G-Node와 제거되는 에지의 선택 방법을 제안하고, 이를 기존의 휴리스틱에 접목한 새로운 휴리스틱을 구현한다. 실험 결과는 이 휴리스틱이 이전 것에 비해 우수함을 나타내는데, 새 지역적 배치 휴리스틱은 17%, 새 전역적 배치 휴리스틱은 14%의 네트워크 구축비용 절감비율의 증가를 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
  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', Algorithmica, Vol.42, pp.109-120, 2005 https://doi.org/10.1007/s00453-004-1133-y
  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
  6. 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
  7. E.J. Cockayne and D.E. Hewgrill, 'Improved Computation of Plane Steiner Minimal Tree', Algorithmica, Vol.7, pp.219-229, 1992 https://doi.org/10.1007/BF01758759
  8. 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
  9. F.K. Hwang, D.S. Richards and P. Winter, 'The Steiner Tree Problem', Annals of Discrete Mathematics, Vol.53, North-Holland, 1992
  10. 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
  11. 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
  12. 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
  13. A. Balakrishnan, T.L. Nagnanti, 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
  14. 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
  15. G.H. Lin and G.L. Xue, 'Steiner Tree Problem with Minimum Number of Steiner Points & Bounded Edge-length', Information Processing Letters, pp.53-57, 1999
  16. 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