Broadcasting and Embedding Algorithms for a Half Hypercube Interconnection Network

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 240)


The half hypercube interconnection network, has been proposed as a new variation of the hypercube, reducing its degree by approximately half with the same number of nodes as an n-dimensional hypercube, Q n . This paper proposes an algorithm for one-to-many broadcasting in an n-dimensional half hypercube, HH n , and examines the embedding between hypercube and half hypercube graphs. The results show that the one-to-many broadcasting time of the HH n can be accomplished in n + 1 when n is an even number and in \( 2 \times \lceil n/ 2\rceil \) when n is an odd number. The embedding of HH n into Q n can be simulated in constant time O(n) and the embedding of Q n into HH n in constant time O(1).


Half hypercube One-to-many broadcasting Embedding 


  1. 1.
    Kim JS, Kim M, Lee HO (2013) Analysis and design of a half hypercube interconnection network. ATACS 2013, LNEE. Springer, Heidelberg (will be appeared)Google Scholar
  2. 2.
    Kim M, Kim DW, Lee HO (2010) Embedding algorithms for star, bubble-sort, rotator-faber-moore, and pancake graphs. HPCTA 2010, LNCS, vol 6082. Springer, Heidelberg, pp 348–357Google Scholar
  3. 3.
    Lee HO, Sim H, Seo JH, Kim M (2010) Embedding algorithms for bubble-sort, macro-star, and transposition graphs. NPC 2010, LNCS, vol 6289. Springer, Heidelberg, pp 134–143Google Scholar
  4. 4.
    Saad Y, Schultz MH (1988) Topological properties of hypercubes. IEEE Trans Comput 37(7):867–872CrossRefGoogle Scholar
  5. 5.
    Seitz CL (1985) The cosmic cube. Commun ACM 26:22–33CrossRefGoogle Scholar
  6. 6.
    Leightoo FT (1992) Introduction to parallel algorithms and architectures: arrays, hypercubes. Morgan Kaufmann Publishers, San FranciscoGoogle Scholar
  7. 7.
    Mendia VE, Sarkar D (1992) Optimal broadcasting on the star graph. IEEE Trans Parallel Distrib Syst 3(4):389–396CrossRefMathSciNetGoogle Scholar
  8. 8.
    Feng T (1981) A survey of interconnection networks. IEEE computer 14:12–27Google Scholar
  9. 9.
    Bettayel S, Cong B, Girou M, Sudborough IH (1996) Embedding star networks into hypercubes. IEEE Trans Comput 45(2):186–194CrossRefMathSciNetGoogle Scholar
  10. 10.
    Hedetniemi SM, Hedetniemi T, Liestman AL (1988) A survey of gossiping and broadcasting in communication networks. Networks 18:319–349CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Hamdi M, Song SW (1997) Embedding hierarchical hypercube networks into the hypercube. IEEE Trans Parallel Distrib Syst 8(9):897–902CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht(Outside the USA) 2013

Authors and Affiliations

  1. 1.Department of Computer Science EducationCatholic University of DaeguDaeguSouth Korea
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA
  3. 3.Department of Computer EducationSunchon National UniversitySunchonSouth Korea

Personalised recommendations