The Journal of Supercomputing

, Volume 41, Issue 3, pp 269–286

Perfect load balancing on the star interconnection network



In this paper, we use the regular distribution method to design a perfect load balancing algorithm for an n-star with a maximum error of 1 and a time complexity of 3n(n+1). This algorithm is based on the novel notion of leader trees. A second algorithm proposed in this paper as an enhancement to our first algorithm and uses an arbitrary spanning tree as the leader tree and has a worst time complexity of 2.25n2−3n+0.75. We also discuss the issue of dynamically selecting the leader tree and hybrid load balancing algorithms in general. Furthermore, we present a hybrid algorithm for load balancing on the star interconnection network which benefits from a diffusion load balancing preprocessing phase and shows a smaller mean time complexity than our two first algorithms.


Multicomputers Interconnection networks Star graph Load balancing Hierarchical algorithm Tree embedding 


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  1. 1.
    Al-Ayyoub A, Day K (2003) Node ranking schemes for the star networks. J Parallel Distrib Comput 63:239–250 CrossRefMATHGoogle Scholar
  2. 2.
    Akers SB, Harel D, Krishnamurthy B (1987) The star graph: an attractive alternative to the n-cube. In: Proc international conference on parallel processing, pp 393–400 Google Scholar
  3. 3.
    Bagherzadeh N, Dowd M, Nassif N (1996) Embedding an arbitrary binary tree into the star graph. IEEE Trans Comput 45(4):475–481 CrossRefMATHGoogle Scholar
  4. 4.
    Berenbrink P, Friedetzky T, Martin RA (2005) Dynamic diffusion load balancing. In: ICALP, pp 1386–1398 Google Scholar
  5. 5.
    Berenbrink P, Friedetzky T, Zengjian H (2006) A new analytical method for parallel, diffusion-type load balancing. In: Parallel and distributed processing symposium, IPDPS, April 2006, 10 pp Google Scholar
  6. 6.
    Chen TS, Tseng YC, Sheu JP (1996) Balanced spanning trees in complete and incomplete star graphs. IEEE Trans Parallel Distrib Syst 7(7):717–723 CrossRefGoogle Scholar
  7. 7.
    Chen TS, Wang NC (2005) Optimal broadcasting on incomplete star graph interconnection networks. J Syst Architect 51(2):143–150 CrossRefGoogle Scholar
  8. 8.
    Elsässer R, Monien B, Preis R (2002) Diffusion schemes for load balancing on heterogeneous networks. Theory Comput Syst 35(3):305–320 CrossRefMATHGoogle Scholar
  9. 9.
    Elsasser R, Monien B, Schamberger S (2004) Load balancing in dynamic networks. In: Parallel Architectures, Algorithms and Networks, 2004, pp 193–200 Google Scholar
  10. 10.
    Jan GE, Hwang YS (2003) An efficient algorithm for perfect load balancing on hypercube multiprocessors. J Supercomput 25:5–15 CrossRefMATHGoogle Scholar
  11. 11.
    Jwo JS, Lakshmivarahan S, Dhall SK (1991) Embedding of cycles and grids in star graphs. J Circ Syst Comput 1(1):43–74 CrossRefGoogle Scholar
  12. 12.
    Plaxton GC (1989) Load balancing, selection and sorting on the hypercube. In: Proc of the 1st ACM symposium on parallel algorithms and architectures, June 1989, pp 64–73 Google Scholar
  13. 13.
    Qiu K, Akl SG (1994) Load balancing, selection, and sorting on the star and pancake interconnection networks. Parallel Algorithm Appl 2:27–42 MATHGoogle Scholar
  14. 14.
    Rotaru T, Nägeli HH (2004) Dynamic load balancing by diffusion in heterogeneous systems. J Parallel Distrib Comput 64(4):481–497 CrossRefMATHGoogle Scholar
  15. 15.
    Sakia DK, Sen RK (1996) Two ranking schemes for efficient computation on the star interconnection network. IEEE Trans Parallel Distrib Syst 7(4):321–327 CrossRefGoogle Scholar
  16. 16.
    Shi W, Srimani PK (2005) Leader election in hierarchical star network. J Parallel Distrib Comput 65(11):1435–1442 CrossRefMATHGoogle Scholar
  17. 17.
    Tseng CY, Chang SH, Sheu JP (1997) Fault-tolerant ring embedding in a star graph with both link and node failure. IEEE Trans Parallel Distrib Syst 8(12):1185–1195 CrossRefGoogle Scholar
  18. 18.
    Tseng YC, Sheu JP (1997) Toward optimal broadcast in a star graph using multiple spanning trees. IEEE Trans Comput 46(5) Google Scholar
  19. 19.
    Willebeek-LeMair MH, Reeves AP (1993) Strategies for dynamic load balancing on highly parallel computers. IEEE Trans Parallel Distrib Syst 4(9):979 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.IPM School of Computer ScienceTehranIran
  2. 2.Sharif University of Technology & IPMTehranIran
  3. 3.Queens UniversityKingstonCanada

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