Reliable Minimum Finding Comparator Networks

We consider the problem of constructing reliable minimum nd-ing networks built from unreliable comparators. In case of a faulty compara-tor inputs are directly output without comparison. Our main result is the rst 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(dlog ne + 2k; log n + k log log n k+1). We also describe a network whose depth nearly matches the lower bound. The lower bounds should be compared with the rst nontrivial upper bound O(log n + k log log n log k) on the depth of k-fault tolerant sorting networks that was recently derived by Leighton and Ma 6].