광 베니언-유형 교환 망에서의 누화를 회피하기 위한 교환소자를 달리하는 멀티캐스트 스케줄링(제2부):스케줄링 길이 및 넌블럭킹 특성

Switching Element-Disjoint Multicast Scheduling for Avoiding Crosstalk in Photonic Banyan-Type Switching Networks (Part II):Scheduling Lengths and Nonblocking Property

  • 차영환 (상지대학교 컴퓨터정보공학부)
  • 발행 : 2001.12.31

초록

선행 논문(제1부)[13]에서는 광 베니언-형 교환 망에 있어 누화를 야기하는 멀티캐스트 접속들간의 관계를 그래프로 표현하고, 해당 그래프의 차수의 상한을 제시하였다. 본 논문(제2부)에서는 교환소자를 달리하는 멀티캐스팅의 스케줄링에서의 라우팅 횟수 즉, 스케줄링 길이에 대해 다룬다. 최적의 스케줄링 길이를 구하는 문제는 NP-complete이므로 최적 길이의 상한의 두 배 이내의 길이를 제공하는 근사 알고리즘을 제시한다. 아울러, 링크를 달리하는(즉, 넌블럭킹) 멀티캐스팅에 관한 스케줄링 길이를 고찰한다. 얻어진 스케줄링 길이 하에서 다양한 넌블럭킹 베니언-형 멀티캐스팅 망들을 규명한다.

In our predecessor paper(Part I)[13], we introduced a graph that represents the crosstalk relationship among multicast connections in the photonic Banyan-type switching network, and found the upper bound on the degree of it. In this paper(Part II), we consider the number of routing rounds(i.e., scheduling length) required for SE(switching element)-disjoint multicasting in photonic Banyan-type switching networks. Unfortunately, the problem to find an optimal scheduling length is NP-complete thus, we propose an approximation algorithm that gives its scheduling length is always within double of the upper bound on the optimal length. We also study the scheduling length on the Iink-disjoint(i.e., nonblocking) multicasting. Various nonblocking Banyan-type multicasting networks are found under the scheduling lengths.

키워드

참고문헌

  1. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Reading: Addison-Wesley, 1974
  2. J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, New York: American Elsevier, 1976
  3. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, San Francisco: Freeman and Company, 1979
  4. T. T. Lee, 'Non-blocking copy networks for multicast packet switching,' IEEE J. Selected Areas in Commun., vol. 6, no. 9, pp. 1445-1467, Dec. 1988 https://doi.org/10.1109/49.12873
  5. C.-T. Lea, 'Bipartite graph design principle for photonic switching systems,' IEEE Trans. Commun., vol. COM-38, no.4, pp.529-538, Apr. 1990 https://doi.org/10.1109/26.52664
  6. C.-T. Lea, 'Multi-$log_2N$ networks and their applications in high-speed electronic and photonic switching systems,' IEEE Trans. Commun., vol. COM-38, no. 10, pp. 1740-1749, Oct. 1990 https://doi.org/10.1109/26.61445
  7. Y. Pan, C. Qiao, and Y. Yang, 'Optical multistage interconnection networks: new challenges and approaches,' IEEE Commun. Maga., vol. 37, no. 2, pp. 50-56, Feb. 1999 https://doi.org/10.1109/35.747249
  8. C. Qiao and L. Zhou, 'Scheduling switching element(SE) disjoint connections in stage-controlled photonic banyans,' IEEE Trans. Commun. vol. COM-47, no. 1, pp. 139-148, Jan. 1999 https://doi.org/10.1109/26.747821
  9. R. K. Pankaj 'Wavelength requirements for multicasting in all-optical networks,' IEEE/ACM Trans. Networking, vol. 7, no. 3, pp. 414-424, Jun. 1999 https://doi.org/10.1109/90.779211
  10. Y. Tscha and K,-H Lee, 'Yet another result on multi-$log_{2}$N networks,' IEEE Trans. Commun., vol. COM-47, no. 9, pp. 1425-1431, 1999 https://doi.org/10.1109/26.789678
  11. M. Vaez and C.-T. Lea, 'Strictly nonblocking directional-coupler-based switching networks under crosstalk constraint,' IEEE Trans. Commun., vol. 48, no. 2, pp. 316-323, Feb. 2000 https://doi.org/10.1109/26.823564
  12. M. Vaez and C.-T. Lea, 'Wide-sense nonblocking Banyan-type switching systems based on directional couplers,' IEEE J. Select. Areas Commun., vol. 16, pp. 1327-1332, Sept. 1998 https://doi.org/10.1109/49.725200
  13. Y. Tscha, 'SE-disjoint multicast scheduling for avoiding crosstalk in photonic Banyan-type switching networks(Part I): graph theoretic analysis of crosstalk relationship,' Journal of KISS: Information Networking, Vol. 28, no. 3, pp. 447-453, Sept. 2001