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Sorry if this question was already asked. I'm new to sequence analysis, I'm using TraMineR to analyze some sequences with the Optimal Matching. But I need to know the maximum possible cost that can result from using the OM.

I'm using an alphabet like: A,B,C,D,E,F and I have defined a substitution matrix.

Is there any way to know the maximum possible distance or cost of a sequence without creating all possible sequences of the alphabet?

Thanks in advance for your help.

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The answer is given in

Gabadinho, A., Ritschard, G., Müller, N.S. & Studer, M. (2011), Analyzing and visualizing state sequences in R with TraMineR, Journal of Statistical Software. Vol. 40(4), pp. 1-37.

which is distributed as a vignette with the TraMineR package. Page 29, it is stated that the maximum OM distance between two sequences $x$ and $y$ is

$D_{max}=\min(\ell_{x},\ell_{y}) \cdot \min\big(2{c_I}, \max(S)\big) + c_{I} |\ell_{x}-\ell_{y}|$

where $\ell_x$ and $\ell_y$ are the sequence lengths, $c_I$ the indel cost and $S$ the substitution cost matrix.

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