Depth optimal sorting networks resistant to k passive faults

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:416806

Piotrow, M ^[1]

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1. Univ. of Wroclaw (Poland)

In this paper, we study the problem of constructing a sorting network that is tolerant to faults and whose running time (i.e. depth) is as small as possible. We consider the scenario of worst-case comparator faults and follow the model of passive comparator failure proposed by Yao and Yao, in which a faulty comparator outputs directly its inputs without comparison. Our main result is the first construction of an N-input, k-fault-tolerant sorting network that is of an asymptotically optimal depth {theta}(log N+k). That improves over the recent result of Leighton and Ma, whose network is of depth O(log N + k log log N/log k). Actually, we present a fault-tolerant correction network that can be added after any N-input sorting network to correct its output in the presence of at most k faulty comparators. Since the depth of the network is O(log N + k) and the constants hidden behind the {open_quotes}O{close_quotes} notation are not big, the construction can be of practical use. Developing the techniques necessary to show the main result, we construct a fault-tolerant network for the insertion problem. As a by-product, we get an N-input, O(log N)-depth INSERT-network that is tolerant to random faults, thereby answering a question posed by Ma in his PhD thesis. The results are based on a new notion of constant delay comparator networks, that is, networks in which each register is used (compared) only in a period of time of a constant length. Copies of such networks can be put one after another with only a constant increase in depth per copy.

• OSTI ID: 416806
• Report Number(s): CONF-960121--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
FAULT TOLERANT COMPUTERS
FAULT TREE ANALYSIS
NETWORK ANALYSIS
SORTING