Abstract
We consider the problem of constructing reliable minimum finding networks built from unreliable comparators. In case of a faulty comparator inputs are directly output without comparison. Our main result is the first nontrivial lower bound on depths of networks computing minimum among n > 2 items in the presence of k > 0 faulty comparators. We prove that the depth of any such network is at least max([log n] + 2k, log n + k log logn/k+1). We also describe a network whose depth nearly matches the lower bound. The lower bounds should be compared with the first nontrivial upper bound O(log n + k log log n/logk) on the depth of k-fault tolerant sorting networks that was recently derived by Leighton and Ma [6].
Research supported in part by NSERC International Fellowship and by grant KBN 2-2043-92-03.
Research supported in part by NSERC grant OGP 0008136.
Research supported in part by Alexander von Humboldt-Stiftung, Volkswagen Stiftung and the ESPRIT Basic Research Action No. 7141 (ALCOM II).
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© 1994 Springer-Verlag Berlin Heidelberg
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Denejko, P., Diks, K., Pelc, A., Piotrów, M. (1994). Reliable minimum finding comparator networks. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_77
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DOI: https://doi.org/10.1007/3-540-58338-6_77
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