  We present a general approach to the problem of determining the asymptotic
order of the variance of the optimal score between two independent random
sequences defined over an arbitrary finite alphabet. Our general approach is
based on identifying random variables driving the fluctuations of the optimal
score and conveniently choosing functions of them which exhibit certain
monotonicity properties. We show how our general approach establishes a common
theoretical background for the techniques used by Matzinger et al. in a series
of previous articles [6, 8, 20, 24, 26, 37] studying the same problem in
especial cases. Additionally, we explicitely apply our general approach to
study the fluctuations of the optimal score between two random sequences over a
finite alphabet (closing the study as initiated in [26]) and of the length of
the longest common subsequences between two random sequences with a certain
block structure (generalizing part of [37]).
