An O(log n log log n) CRCW PRAM algorithm using O(n/log n) processors
for computing the unique Lyndon factorization of a word of length n ov
er an unbounded alphabet is presented; this improves the bounds given
by Apostolico and Crochemore (1989). Moreover, in the case of fixed al
phabets the CRCW PRAM algorithm is optimal (linear cost), requiring O(
log n) units of time.