Merging and Merge-Sort in a Single Hop Radio Network

  • Marcin Kik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3831)


We present two merging algorithms on a single-channel single-hop radio network without collision detection. The simpler of these algorithms merges two sorted sequences of length n in time 4n with energetic cost for each station \(\approx {\rm lg} {\it n}\). The energetic cost of broadcasting is constant. This yields the merge-sort for n elements in time 2nlg n, where the energetic cost for each station is \(\frac{1}{2}{\rm lg}^{2}{\it n}+\frac{7}{2} {\rm lg}{\it n}\) (the energetic cost of broadcasting is only 2 lg n), which seems to be suitable for practical applications due to its simplicity and low constants. We also present algorithm for merging in time O(nlg*n) with energetic cost O(lg* n).


Radio Network Time Slot Energetic Cost Collision Detection Leader Election 


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  1. 1.
    Ajtai, M., Komlós, J., Szemerédi, E.: Sorting in c logn Parallel Steps. Combinatorica 3, 1–19 (1983)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Batcher, K.E.: Sorting Networks and Their Applications. In: Proceedings of 32nd AFIPS, pp. 307–314 (1968)Google Scholar
  3. 3.
    Blum, M., Floyd, R.W., Pratt, V., Rivest, R.L., Tarjan, R.E.: Time Bounds for Selection. Journal of Computer System Sciences 7(4), 448–461 (1973)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms (1994)Google Scholar
  5. 5.
    Jurdziński, T., Kutyłowski, M., Zatopiański, J.: Efficient Algorithms for Leader Election in Radio Networks. In: ACM PODC 2002, pp. 51–57. ACM Press, New York (2002)CrossRefGoogle Scholar
  6. 6.
    Jurdziński, T., Kutyłowski, M., Zatopiański, J.: Energy-Efficient Size Approximation for Radio Networks with No Collision Detection. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 279–289. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. 7.
    Kutyłowski, M., Letkiewicz, D.: Computing Average Value in Ad Hoc Networks. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 511–520. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Nakano, K., Olariu, S.: Efficient Initialization Protocols for Radio Networks with No Collision Detection. In: ICPP 2000, pp. 263–270. IEEE Computer Society Press, New York (2000)Google Scholar
  9. 9.
    Nakano, K., Olariu, S.: Broadcast-Efficient Protocols for Mobile Radio Networks with Few Channels. IEEE Transactions on Parallel and Distributed Systems 10, 1276–1289 (1999)CrossRefGoogle Scholar
  10. 10.
    Singh, M., Prasanna, V.K.: Optimal Energy Balanced Algorithm for Selection in Single Hop Sensor Network. In: SNPA ICC (May 2003)Google Scholar
  11. 11.
    Singh, M., Prasanna, V.K.: Energy-Optimal and Energy-Balanced Sorting in a Single-Hop Sensor Network. In: PERCOM (March 2003)Google Scholar
  12. 12.
    Compendium of Large-Scale Optimization Problems (DELIS, Subproject 3),

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marcin Kik
    • 1
  1. 1.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWrocławPoland

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