Abstract
In this paper we construct sorting comparator networks which correct a fixed number t of faults in a sorted sequence of length N. We study two kinds of such networks. One construction yields a fault tolerant unit that attached at the end of any comparator sorting network makes the whole network a sorting one resistant to t passive faults. The second network can be used to ‘repair’ a sorted sequence in which at most t entries were changed (no fault tolerance is required). The new results of this paper are constructions of comparator networks of depth 1.44 · log N for these problems which is less than the depths of networks described by previous authors [3],[4],[5]. The construction of the networks is practical for small t. The numbers of comparators used by our networks are shown to be reducible to values optimal up to a constant factor.
Partially supported by KBN grant 8 T11C 032 15 and by University of Wroclaw grant 2320/W/IIn/99.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
. M. Ajtai, J. Komolós, E. Szemerédi, Sorting in clog n parallel steps, Combinatorica 3 (1983), 1–19.
K.E. Batcher, Sorting networks and their applications, in AFIPS Conf. Proc. 32 (1968), 307–314.
M. Kik, M. Kutylowski, M. Piotrów, Correction Networks, in Proc. of 1999 ICPP, 40–47.
M. Piotrów, Depth Optimal Sorting Networks Resistant to k Passive Faults in Proc. 7th SIAM Symposium on Discrete Algorithms (1996), 242–251 (also accepted for SIAM J. Comput.).
M. Schimmler, C. Starke, A Correction Network for N-Sorters, SIAM J. Comput. 18 (1989), 1179–1197.
A.C. Yao, Bounds on Selection Networks, SIAM J. Comput. 9 (1980), 566–582.
A.C. Yao, F.F. Yao, On Fault-Tolerant Networks for Sorting, SIAM J. Comput. 14 (1985), 120–128.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stachowiak, G. (2000). Fibonacci Correction Networks. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_45
Download citation
DOI: https://doi.org/10.1007/3-540-44985-X_45
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67690-4
Online ISBN: 978-3-540-44985-0
eBook Packages: Springer Book Archive