  The problem of the fluctuation of the Longest Common Subsequence (LCS) of two
i.i.d. sequences of length $n>0$ has been open for decades. There exist
contradicting conjectures on the topic. Chvatal and Sankoff conjectured in 1975
that asymptotically the order should be $n^{2/3}$, while Waterman conjectured
in 1994 that asymptotically the order should be $n$. A contiguous substring
consisting only of one type of symbol is called a block. In the present work,
we determine the order of the fluctuation of the LCS for a special model of
sequences consisting of i.i.d. blocks whose lengths are uniformly distributed
on the set $\{l-1,l,l+1\}$, with $l$ a given positive integer. We showed that
the fluctuation in this model is asymptotically of order $n$, which confirm
Waterman's conjecture. For achieving this goal, we developed a new method which
allows us to reformulate the problem of the order of the variance as a
(relatively) low dimensional optimization problem.
