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Scheduling and performance analysis of multicast interconnects


Multicast is an important operation in various emerging computing/networking applications. In particular, many multicast applications require not only multicast capability but also predictable communication performance, such as guaranteed multicast latency and bandwidth, called quality-of-service (QoS). In this paper, we consider scheduling in multicast interconnects, which aims to minimize the multicast latency for a set of multicast requests. Unfortunately, such a problem has been proved to be NP-Complete, which means that it is unlikely to find a fast exact algorithm for the multicast scheduling problem. We then turn to propose a simple, fast greedy multicast scheduling algorithm and derive a lower bound and an upper bound on the performance of the algorithm. As can be seen, while a lower bound is fairly straightforward, the upper bound is much more difficult to obtain. By translating the multicast scheduling problem into a graph theory problem and employing a random graph approach, we are able to obtain a probabilistic upper bound on the performance of the multicast scheduling algorithm. Our analytical and simulation results show that the performance of the proposed multicast scheduling algorithm is quite close to the lower bound and is statistically guaranteed by the probabilistic upper bound.

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  1. 1.

    Andrews M, Khanna S, Kumaran K (1999) Integrated scheduling of unicast and multicast traffic in an input-queued switch. In: Proc of IEEE INFOCOM ’99, 1999, pp. 1144–1151

  2. 2.

    Bellare M, Goldreich O, Sudan M (1995) Free bits, PCP and non-approximability—towards tight results. In: Proc 36th IEEE symposium on foundations of computer science, 1995, pp. 422–431

  3. 3.

    Bollobás B (2001) Random graphs, 2nd edn. Cambridge University Press, Cambridge

  4. 4.

    Bongiovanni G, Coppersmith D, Wong CK (1981) An optimum time slot assignment algorithm for an SS/TDMA system with variable number of transponders. IEEE Trans Commun 29:721–726

  5. 5.

    Chen WT, Sheu PP, Yu JH (1994) Time slot assignment in tdm multicast switching systems. IEEE Trans Commun, 42:149–165,

  6. 6.

    Chung SP, Ross KW (1991) On nonblocking multirate interconnection networks. SIAM J Comput 20(4):726–736

  7. 7.

    Coudert D, Muñoz X (2001) How graph theory can help communications engineering. In: Gautam DK (ed) Broadband optical fiber communications technology. Jalgaon, India, Dec 2001, pp 47–61

  8. 8.

    Erdős P (1947) Some remarks on the theory of graphs. Bull Am Math Soc 53:292–294

  9. 9.

    Erdős P (1959) Graph theory and probability. Can J Math 11:34–38

  10. 10.

    Erdős P (1961) Graph theory and probability II. Can J Math 13:346–352

  11. 11.

    Feldman P, Friedman J, Pippenger N (1988) Wide-sense nonblocking networks. SIAM J Discret Math 1(2):158–173

  12. 12.

    Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of np-completeness. Freeman

  13. 13.

    Giaccone P, Prabhakar B, Shah D (2001) An efficient randomized algorithm for input-queued switch architecture. In: Proc IEEE hot interconnects 9, Stanford, August 2001

  14. 14.

    Hou J, Wang B (2000) Multicast routing and its qos extension: problems, algorithms, and protocols. IEEE Netw 14:22–36

  15. 15.

    Hwang FK, Jajszczyk A (1986) On nonblocking multiconnection networks. IEEE Trans Commun 34:1038–1041

  16. 16.

    Janson S, Łuczak T, Ruciński A (2000) Random graphs. Wiley

  17. 17.

    Jia X, Du D, Hu X, Lee M, Gu J (2001) Optimization of wavelength assignment for QoS multicast in WDM networks. IEEE Trans Commun 49(2)

  18. 18.

    Lee C, Oruc AY (1995) Design of efficient and easily routable generalized connectors. IEEE Trans Commun 43(2-4):646–650

  19. 19.

    Leighton FT (1979) A graph coloring algorithm for large scheduling problems. J Res Natl Bur Stand 84:489–506

  20. 20.

    McKeown N, Mekkittijul A, Anantharam V, Walrand J (1999) Achieving 100% throughput in an input-queued switch. IEEE Trans Commun 47:1260–1267

  21. 21.

    Melen R, Turner JS (1989) Nonblocking multirate networks. SIAM J Comput 18(2):301–313

  22. 22.

    Prabhakar B, McKeown N, Ahuja R (1997) Multicast scheduling for input-queued switches. IEEE J Select Areas Commun 15:855–866

  23. 23.

    Sahasrabuddhe LH, Mukherjee B (2000) Multicast routing algorithms and protocols: a tutorial. IEEE Netw 14:90–102

  24. 24.

    De Werra D (1985) A introduction to timetabling. Eur J Operat Res 19:151–162

  25. 25.

    West DG (1996) Introduction to graph theory. Prentice Hall

  26. 26.

    Yang Y, Wang J, Qiao C (2000) Nonblocking WDM multicast switching networks. IEEE Trans Parallel Distrib Syst 11:1274–1287

  27. 27.

    Yang Y, Masson GM (1991) Nonblocking broadcast switching networks. IEEE Trans Comput 40(9):1005–1015

  28. 28.

    Yang Y, Wang J (2003) Nonblocking k-fold multicast networks. IEEE Trans Parallel Distrib Syst 14(2):131–141

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Author information

Correspondence to Yuanyuan Yang.

Additional information

The research work was supported in part by the U.S. National Science Foundation under grant numbers CCR-0073085 and CCR-0207999.

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Han, G., Yang, Y. Scheduling and performance analysis of multicast interconnects. J Supercomput 40, 109–125 (2007).

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  • Multicast
  • Interconnects
  • Scheduling algorithms
  • Quality-of-service (QoS)
  • Approximation algorithms
  • Conflict graph
  • Random graph