Skip to main content
SpringerLink
Log in

Optimization Problems in Multicast Tree Construction

  • Chapter
Handbook of Optimization in Telecommunications

Abstract

Multicasting is a technique for data routing in networks that allows multiple destinations to be addressed simultaneously. The implementation of multicasting requires, however, the solution of difficult combinatorial optimization problems. In this chapter, we discuss combinatorial issues occurring in the implementation of multicast routing, including multicast tree construction, minimization of the total message delay, center-based routing, and multicast message packing. Optimization methods for these problems are discussed and the corresponding literature reviewed. Mathematical programming as well as graph models for these problems are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • L. Aguilar, J.J. Garcia-Luna-Aceves, D. Moran, E.J. Graighill, and R. Brungardt. Architecture for a multimedia teleconferencing system. In Proceedings of the ACM SIGCOMM, pages 126–136, Baltimore, Maryland, 1986. Association for Computing Machinery.

    Google Scholar 

  • M. Baldi, Y. Ofek, and B. Yener. Adaptive real-time group multicast. In Proceedings of IEEE INFOCOM’97, page 683, 1997.

    Google Scholar 

  • A. Ballardie, P. Francis, and J. Crowcroft. Core-based trees (CBT)-An architecture for scalable inter-domain multicast routing. Computer Communication Review, 23(4):85–95, 1993.

    Article  Google Scholar 

  • Z. Baoxian, L. Yue, and C. Changjia. An efficient delay-constrained multicast routing algorithm. In International Conference on Communication Technologies (ICCT 2000), page S07.2, 2000.

    Google Scholar 

  • F. Bauer. Multicast routing in point-to-point networks under constraints. PhD thesis, University of California, Santa Cruz, 1996.

    Google Scholar 

  • F. Bauer and A. Varma. Degree-constrained multicasting in point-to-point networks. In Proceedings IEEE INFOCOM’ 95, The Conference on Computer Communications, pages 369–376, 1995.

    Google Scholar 

  • F. Bauer and A. Varma. ARIES: A rearrangeable inexpensive edge-based on-line Steiner algorithm. IEEE Journal of Selected Areas in Communications, 15(3):382–397, 1997.

    Article  Google Scholar 

  • M. Bazaraa, J. Jarvis, and H. Sherali. Linear Programming and Network Flows. John Wiley and Sons, 2nd edition, 1990.

    Google Scholar 

  • R. Bellman. Dynamic Programming. Princeton University Press, Princeton, NJ, 1957.

    Google Scholar 

  • L.T.M. Berry. Graph theoretic models for multicast communications. Computer Networks and ISDN Systems, 20(1):95–99, 1990.

    Article  MathSciNet  Google Scholar 

  • K. Bharath-Kumar and J.M. Jaffe. Routing to multiple destinations in computer networks. IEEE Transactions on Communications, 31(3):343–351, 1983.

    Article  MATH  Google Scholar 

  • D. Blokh and G. Gutin. An approximate algorithm for combinatorial optimization problems with two parameters. Australasian J. Combin., 14:157–164, 1996.

    MATH  MathSciNet  Google Scholar 

  • K.L. Calvert, E.W. Zegura, and M.J. Donahoo. Core selection methods for multicast routing. In IEEE ICCCN’95, pages 638–642, Las Vegas, Nevada, 1995. IEEE.

    Google Scholar 

  • K. Carlberg and J. Crowcroft. Building shared trees using a one-to-many joining mechanism. ACM Computer Communication Review, 27(1):5–11, January 1997.

    Article  Google Scholar 

  • G. Chen, M. Houle, and M. Kuo. The Steiner problem in distributed computing systems. Information Sciences, 74(1):73–96, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Chen, O. Günlük, and B. Yener. Optimal packing of group multicastings. In Proc. IEEE INFOCOM’98, pages 980–987, 1998.

    Google Scholar 

  • C. Chiang, M. Gerla, and L. Zhang. Adaptive shared tree multicast in mobile wireless networks. In Proceedings of GLOBECOM’98, pages 1817–1822, 1998.

    Google Scholar 

  • G.V. Chockler, N. Huleihel, I. Keidar, and D. Dolev. Multimedia multicast transport service for groupware. In TINA Conference on the Convergence of Telecommunications and Distributed Computing Technologies, pages 43–54, 1996.

    Google Scholar 

  • C.H. Chow. On multicast path finding algorithms. In Proc. IEEE INFOCOMM’91, pages 1274–1283, 1991.

    Google Scholar 

  • S.-J. Chung, S.-P. Hong, and H.-S. Huh. A fast multicast routing algorithm for delay-sensitive applications. In IEEE GLOBECOM’97, pages 1898–1902, 1997.

    Google Scholar 

  • R. Correa, F. Gomes, C.A.S. Oliveira, and P.M. Pardalos. A parallel implementation of an asynchronous team to the point-to-point connection problem. Parallel Computing, 29(4):447–466, 2003.

    Article  MathSciNet  Google Scholar 

  • Y. Dalai and R. Metcalfe. Reverse path forwarding of broadcast packets. Communications of the ACM, 21(12), 1978.

    Google Scholar 

  • S. Deering and D. Cheriton. Multicast routing in datagram internetworks and extended LANs. ACM Transactions on Computer Systems, 8(2):85–110, 1990.

    Article  Google Scholar 

  • S. Deering, D. Estrin, D. Farinacci, V. Jacobson, C.-G. Liu, and L. Wei. An architecture for wide-area multicast routing. Computer Communication Review, 24(4): 126–135, 1994.

    Article  Google Scholar 

  • S. Deering, D.L. Estrin, D. Farinacci, V. Jacobson, C.-G. Liu, and L. Wei. The PIM architecture for wide-area multicast routing. IEEE/ACM Transactions on Networking, 4(2): 153–162, 1996.

    Article  Google Scholar 

  • E.W. Dijkstra. A note on two problems in connexion with graphs. Numer. Math., 1: 269–271, 1959.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Doar and I. Leslie. How bad is naive multicast routing. In Proceedings of the IEEE INFOCOM, pages 82–89, Los Alamitos, Calif, USA, 1993. IEEE Comput. Soc. Press.

    Google Scholar 

  • D.-Z. Du, B. Lu, H. Ngo, and P.M. Pardalos. Steiner tree problems. In C.A. Floudas and P.M. Pardalos, editors, Encyclopedia of Optimization, volume 5, pages 227–290. Kluwer Academic Publishers, 2001.

    Google Scholar 

  • D.-Z. Du and P.M. Pardalos, editors. Network Optimization Problems: Algorithms, Complexity and Applications. World Scientific, 1993a.

    Google Scholar 

  • D.-Z. Du and P.M. Pardalos. Subset interconnection designs: Generalizations of spanning trees and Steiner trees. In Network Optimization Problems, pages 111–124. World Scientific, 1993b.

    Google Scholar 

  • C.A. Ellis, S.J. Gibbs, and G.L. Rein. Groupware: Some issues and experiences. Commun. ACM, 34(1):39–58, 1991.

    Article  Google Scholar 

  • H. Eriksson. MBONE — the multicast backbone. Communications of ACM, 37(8): 54–60, 1994.

    Article  MathSciNet  Google Scholar 

  • U. Feige. A threshold of In n for approximating set cover. Journal of the ACM, 45(4): 634–652, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  • G. Feng and T. Peter Yum. Efficient multicast routing with delay constraints. International Journal of Communication Systems, 12:181–195, 1999.

    Article  Google Scholar 

  • A. Forsgren and M. Prytz. Dimensioning multicast-enabled communications networks. Networks, 39:216–231, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  • A.J. Frank, L.D. Wittie, and A.J. Bernstein. Multicast communication on network computers. IEEE Software, 2(3):49–61, 1985.

    Article  Google Scholar 

  • R.G. Gallager, PA. Humblet, and P.M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Programming Languages and Systems, 5(1): 66–77, 1983.

    Article  MATH  Google Scholar 

  • M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman and Company, 1979.

    Google Scholar 

  • M.X. Goemans and D.P Williamson. A General Approximation Technique for Constrained Forest Problems. SIAM J. Comp., 24(2):296–317, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  • F.C. Gomes, C.N. Meneses, A.R.G. Lima, and C.A.S. Oliveira. Asynchronous organizations for solving the point-to-point connection problem. In Proc. of the Intl. Conference on Multiagents Systems (ICMAS), pages 144–149. IEEE Computer Society, 1998.

    Google Scholar 

  • L. Han and N. Shahmehri. Secure multicast software delivery. In IEEE 9th International Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises (WET ICE’00), pages 207–212, 2000.

    Google Scholar 

  • S. Hong, H. Lee, and B.H. Park. An efficient multicast routing algorithm for delay-sensitive applications with dynamic membership. In Proceedings of IEEE INFOCOM’98, pages 1433–1440, 1998.

    Google Scholar 

  • F. Hwang and D. Richards. Steiner tree problems. Networks, 22:55–89, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  • F. Hwang, D.S. Richards, and P. Winter. The Steiner tree problem, volume 53 of Annals of Discrete Mathematics. North-Holland, 1992.

    Google Scholar 

  • IBM. Reliable multicast messaging, 2005. Available at http://www.haifa.il.ibm.com/projects/software/rmsdk.

  • Y. Im, Y. Lee, S. Wi, and Y. Choi. A delay constrained distributed multicast routing algorithm. Computer Communications, 20(1):60–66, 1997.

    Article  Google Scholar 

  • X. Jia. A distributed algorithm of delay-bounded multicast routing for multimedia applications in wide area networks. IEEE/ACM Transactions on Networking, 6(6): 828–837, 1998.

    Article  Google Scholar 

  • X. Jia, N. Pissinou, and K. Makki. A real-time multicast routing algorithm for multimedia applications. Computer Commun. J., 20(12):1098–1106, 1997.

    Article  Google Scholar 

  • X. Jiang. Routing broadband multicast streams. Computer Communications, 15(1): 45–51, 1992.

    Article  Google Scholar 

  • Chee Kheong, David Siew, and Gang Feng. Efficient setup for multicast connections using tree-caching. In Proceedings IEEE INFOCOM 2001, pages 249–258, 2001.

    Google Scholar 

  • V. Kompella, J. Pasquale, and G. Polyzos. Multicasting for multimedia applications. In Proceedings of IEEE INFOCOM’92, pages 2078–2085, 1992.

    Google Scholar 

  • V. Kompella, J. Pasquale, and G. Polyzos. Two distributed algorithms for the constrained Steiner tree problem. In Proceedings of the Second International Conference on Computer Communications and Networking (ICCCN’93), pages 343–349, 1993a.

    Google Scholar 

  • V.P. Kompella, J.C. Pasquale, and G.C. Polyzos. Multicast routing for multimedia communication. IEEE/ACM Trans. Networking, l(3):286–292, 1993b.

    Article  Google Scholar 

  • V.P. Kompella, J.C. Pasquale, and G.C. Polyzos. Optimal multicast routing with quality of service constraints. Journal of Network and Systems Management, 4(2): 107–131, 1996.

    Article  Google Scholar 

  • L. Kou, G. Markowsky, and L. Berman. A fast algorithm for Steiner trees. Acta Informatica, 15:141–145, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  • C. Li, S. McCormick, and D. Simchi-Levi. The point-to-point delivery and connection problems: Complexity and algorithms. Discrete Applied Math., 36:267–292, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  • Z. Li and P. Mohapatra. QMBF: A QoS-aware multicast routing protocol. Computer Communications Journal, 26(6):611–621, 2003.

    Article  Google Scholar 

  • Z.M. Mao, D. Johnson, O. Spatscheck, J E. van der Merwe, and J. Wang. Efficient and robust streaming provisioning in VPNs. In Proceedings of the WWW2003, Budapest, Hungary, May 2003.

    Google Scholar 

  • C.N. Meneses, C.A.S. Oliveira, and P.M. Pardalos. A branch-and-cut to the point-to-point connection problem on multicast networks. In F. Giannessi and A. Maugeri, editors, Variational Analysis and Applications, page 1084. Kluwer Academic Publishers, Dordrecht, 2004.

    Google Scholar 

  • J. Moy. Multicast extensions to OSPF, RFC 1584 — IETF network working group. On-line document: http://www.ietf.org/, 1994a.

  • J. Moy. OSPF version 2, RFC 1583 — IETF network working group. On-line document: http://www.ietf.org/, 1994b.

  • M.G. Natu. Network Loading and Connection Problems. PhD thesis, Operations Research Dept., North Carolina State University, 1995.

    Google Scholar 

  • C. Noronha and F. Tobagi. Optimum routing of multicast streams. In IEEE INFOCOM’94, pages 865–873, 1994.

    Google Scholar 

  • C.A.S. Oliveira and P.M. Pardalos. Construction algorithms and approximation bounds for the streaming cache placement problems in multicast networks. Cybernetics and systems Analysis, 41, 2005. To appear.

    Google Scholar 

  • C.A.S. Oliveira, P.M. Pardalos, O.A. Prokopyev, and M.G.C. Resende. Streaming cache placement problems: Complexity and algorithms. Technical report, University of Florida, 2003.

    Google Scholar 

  • P.M. Pardalos and D.-Z. Du, editors. Network Design: Connectivity and Facilities Location, volume 40 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1998.

    Google Scholar 

  • P.M. Pardalos, F. Hsu, and S. Rajasekaran, editors. Mobile Networks and Computing, volume 52 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 2000.

    Google Scholar 

  • P.M. Pardalos and B. Khoury. An exact branch and bound algorithm for the Steiner problem in graphs. In D.-Z. Du & M. Li, editor, Proceedings of COCOON’95, volume 959 of Lecture Notes in Computer Science, pages 582–590. Springer-Verlag, Xi’an, China, 1995.

    Google Scholar 

  • P.M. Pardalos and B. Khoury. A heuristic for the Steiner problem on graphs. Comp. Opt. & Appl., 6:5–14, 1996.

    MATH  MathSciNet  Google Scholar 

  • P.M. Pardalos, B.N. Khoury, and D.-Z. Du. A test problem generator for the steiner problem in graphs. ACM Transactions on Mathematical Software, 19(4):509–522, 1993.

    Article  MATH  Google Scholar 

  • J. Park and C. Park. Development of a multi-user & multimedia game engine based on TCP/IP. In Proceedings of IEEE Pacific Rim Conference on Communications Computers and Signal Processing, pages 101–104, Victoria, B.C. Canada, 1997.

    Google Scholar 

  • J. Pasquale, G. Polyzos, and G. Xylomenos. The multimedia multicasting problem. ACM Multimedia Systems Journal, 6(1):43–59, 1998.

    Article  Google Scholar 

  • P. Paul and S.V. Raghavan. Survey of multicast routing algorithms and protocols. In Proceedings of the Fifteenth International Conference on Computer Communication (ICCC 2002), pages 902–926, 2002.

    Google Scholar 

  • V. Priwan, H. Aida, and T. Saito. The multicast tree based routing for the complete broadcast multipoint-to-multipoint communications. IEICE Transactions on Communications, E78-B(5):720–728, 1995.

    Google Scholar 

  • M. Prytz. On optimization in Design of Telecommunications Networks with Multicast and Unicast Traffic. PhD thesis, Dept. of Mathematics, Royal Institute of Technology, Stockholm, Sweden, 2002.

    Google Scholar 

  • M. Prytz and A. Forsgren. Dimensioning of a multicast network that uses shortest path routing distribution trees. Technical Report TRITA-MAT-2002-OS1, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden, 2002.

    Google Scholar 

  • S. Ramanathan. Multicast tree generation in networks with asymmetric links. IEEE/ACM Trans. Networking, 4(4):558–568, 1996.

    Article  MathSciNet  Google Scholar 

  • G.N. Rouskas and I. Baldine. Multicast routing with end-to-end delay and delay variation constraints. In IEEE INFOCOM’96, pages 353–360, 1996.

    Google Scholar 

  • S. Sabri and B. Prasada. Video conferencing systems. Proc. of the IEEE, 73(4):671–688, 1985.

    Article  Google Scholar 

  • H.F. Salama, D.S. Reeves, and Y. Viniotis. Shared multicast trees and the center selection problem: A survey. Technical Report TR-96/27, Dept. of Electrical and Computer Engineering, NCSU, 1996.

    Google Scholar 

  • H.F. Salama, D.S. Reeves, and Y. Viniotis. The delay-constrained minimum spanning tree problem. In 2nd IEEE Symposium on Computers and Communications (ISCC’97), pages 699–704. IEEE Computer Society, 1997a.

    Google Scholar 

  • H.F. Salama, D.S. Reeves, and Y. Viniotis. Evaluation of multicast routing algorithms for real-time communication on high-speed networks. IEEE Journal on Selected Areas In Communications, 15(3):332–345, 1997b.

    Article  Google Scholar 

  • C. Semeria and T. Maufer. Introduction to IP multicast routing. Internet draft (IETF), 1996.

    Google Scholar 

  • A. Shaikh and K.G. Shin. Destination-driven routing for low-cost multicast. IEEE Journal of Selected Areas in Communications, 15(3):373–381, 1997.

    Article  Google Scholar 

  • R. Sriram, G. Manimaran, and C. Siva Ram Murthy. Algorithms for delay-constrained low-cost multicast tree construction. Computer Communications, 21(18): 1693–1706, 1998.

    Article  Google Scholar 

  • R. Sriram, G. Manimaran, and C. Siva Ram Murthy. A rearrangeable algorithm for the construction of delay-constrained dynamic multicast trees. IEEE/ACM Transactions on Networking, 7(4):514–529, 1999.

    Article  Google Scholar 

  • H. Takahashi and A. Matsuyama. An approximate solution for the Steiner problem in graphs. Mathematica Japonica, 24(6):573–577, 1980.

    MATH  MathSciNet  Google Scholar 

  • S.N. Talukdar and P.S. de Souza. Asynchronous Teams. In Second SIAM Conf. on Linear Algebra: Signals, Systems, and Control, San Francisco, 1990.

    Google Scholar 

  • T.M. Thomas II. OSPF network design solutions. Cisco Systems, 1998.

    Google Scholar 

  • D. Waitzman, C. Partridge, and S. Deering. Distance Vector Multicast Routing Protocol, RFC 1075 — IETF Network Working Group. On-line document: http://www.ietf.org/,1988.

  • D. Wall. Mechanisms for Broadcast and selective broadcast. PhD thesis, Stanford University, 1980.

    Google Scholar 

  • D.W. Wall. Mechanisms for broadcast and selective broadcast. PhD thesis, Computer Science Department, Stanford University, 1982.

    Google Scholar 

  • P.-J. Wan, D.-Z. Du, and Panos M. Pardalos, editors. Multichannel Optical Networks: Theory and Practice, volume 46 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1998.

    Google Scholar 

  • C.-F. Wang, C.-T. Liang, and R.-. Jan. Heuristic algorithms for packing of multiple-group multicasting. Computers & Operations Research, 29(7):905–924, 2002.

    Article  MATH  Google Scholar 

  • B.M. Waxman. Routing of multipoint connections. IEEE Journal on Selected Areas in Communications, 6(9): 1617–1622, 1988.

    Article  Google Scholar 

  • L. Wei and D. Estrin. The trade-offs of multicast trees and algorithms, 1994.

    Google Scholar 

  • S. Wi and Y. Choi. A delay-constrained distributed multicast routing algorithm. In Proceeding of the Twelfth International Conference on Computer Communication (ICCC’95), pages 883–838, 1995.

    Google Scholar 

  • P. Winter. Steiner problem in networks: A survey. Networks, 17:129–167, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  • P. Winter and J.M. Smith. Path-distance heuristics for the Steiner problem in undirected networks. Algorithmica, pages 309–327, 1992.

    Google Scholar 

  • W. De Zhong, Y. Onozato, and J. Kaniyil. A copy network with shared buffers for large-scale multicast ATM switching. IEEE/ACM Transactions on Networking, 1(2): 157–165, 1993.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, 74078, USA

    Carlos A.S. Oliveira

  2. Center for Applied Optimization Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos

  3. Internet & Network Systems Research Center AT&T Labs Research, Shannon Laboratory, Florham Park, NJ, 07932, USA

    Mauricio G.C. Resende

Authors
  1. Carlos A.S. Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mauricio G.C. Resende
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. AT&T Labs Research, Florham Park, New Jersey

    Mauricio G. C. Resende

  2. University of Florida, Gainesville, Florida

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Oliveira, C.A., Pardalos, P.M., Resende, M.G. (2006). Optimization Problems in Multicast Tree Construction. In: Resende, M.G.C., Pardalos, P.M. (eds) Handbook of Optimization in Telecommunications. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30165-5_25

Download citation

Publish with us

Policies and ethics

Search

Navigation