Av. Goldberg et al., A PARALLEL ALGORITHM FOR RECONFIGURING A MULTIBUTTERFLY NETWORK WITH FAULTY SWITCHES, I.E.E.E. transactions on computers, 43(3), 1994, pp. 321-326
This paper describes a deterministic algorithm for reconfiguring a mul
tibutterfly network with faulty switches. Unlike previous reconfigurat
ion algorithms, the algorithm is performed entirely by the network, wi
thout the aid of any off-line computation, even though many of the swi
tches may be faulty. The algorithm reconfigures an N-input multibutter
fly network in O(log N) time. After reconfiguration, the multibutterfl
y can tolerate f worst-case faults and still route any permutation bet
ween some set of N - O(f) inputs and N - O(f) outputs in O(logN) time.