Sorting Long Sequences in a Single Hop Radio Network

  • Marcin Kik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


We propose an algorithm for merging two sorted sequences of length k Open image in new window m stored in two sequences of m stations of single-hop single-channel radio network, where each station stores a block of of k consecutive elements. The time and energetic cost of this algorithm are 6m Open image in new window k+8m–4 and 8k+4⌈log2(m+1)⌉+6, respectively. This algorithm can be applied for sorting a sequence of length N=k Open image in new window n in a network consisting of n stations with memory limited by Θ(k) words. For \(k=\Omega(\lg n)\), the energetic cost of such sorting is \(O(k\cdot\lg n)\) and the time is \(O(N\lg n)\). Moreover, the constants hidden by the big “Oh” are reasonably small, to make the algorithm attractive for practical applications.


Time Slot Energetic Cost Merging Algorithm Comparator Network Batcher Algorithm 
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  1. 1.
    Ajtai, M., Komlós, J., Szemerédi, E.: Sorting in c logn parallel steps. Combinatorica 3, 1–19 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Batcher, K.E.: Sorting networks and their applications. In: Proceedings of 32nd AFIPS, pp. 307–314 (1968)Google Scholar
  3. 3.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms (1994)Google Scholar
  4. 4.
    Kik, M.: Merging and Merge-sort in a Single Hop Radio Network. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 341–349. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Knuth, D.E.: The Art of Computer Programming. Sorting and Searching, vol. 3. Addison-Wesley, Reading (1973)Google Scholar
  6. 6.
    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
  7. 7.
    Nakano, K., Olariu, S., Zomaya, A.Y.: Energy-Efficient Permutation Routing in Radio Networks. IEEE Transactions on Parallel and Distributed Systems 12, 544–557 (2001)CrossRefGoogle Scholar
  8. 8.
    Singh, M., Prasanna, V.K.: Optimal Energy Balanced Algorithm for Selection in Single Hop Sensor Network. In: SNPA ICC (May 2003)Google Scholar
  9. 9.
    Singh, M., Prasanna, V.K.: Energy-Optimal and Energy-Balanced Sorting in a Single-Hop Sensor Network. In: PERCOM (March 2003)Google Scholar
  10. 10.
    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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