Abstract
We propose an algorithm for merging two sorted sequences of length k 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 k+8m–4 and 8k+4⌈log2(m+1)⌉+6, respectively. This algorithm can be applied for sorting a sequence of length N=k 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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Supported by the European Union within the 6th Framework Programme under contract 001907 (DELIS).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ajtai, M., Komlós, J., Szemerédi, E.: Sorting in c logn parallel steps. Combinatorica 3, 1–19 (1983)
Batcher, K.E.: Sorting networks and their applications. In: Proceedings of 32nd AFIPS, pp. 307–314 (1968)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms (1994)
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)
Knuth, D.E.: The Art of Computer Programming. Sorting and Searching, vol. 3. Addison-Wesley, Reading (1973)
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)
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)
Singh, M., Prasanna, V.K.: Optimal Energy Balanced Algorithm for Selection in Single Hop Sensor Network. In: SNPA ICC (May 2003)
Singh, M., Prasanna, V.K.: Energy-Optimal and Energy-Balanced Sorting in a Single-Hop Sensor Network. In: PERCOM (March 2003)
Compendium of Large-Scale Optimization Problems (DELIS, Subproject 3), http://ru1.cti.gr/delis-sp3/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kik, M. (2006). Sorting Long Sequences in a Single Hop Radio Network. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_50
Download citation
DOI: https://doi.org/10.1007/11821069_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37791-7
Online ISBN: 978-3-540-37793-1
eBook Packages: Computer ScienceComputer Science (R0)