  A square symmetric matrix is a Robinson similarity matrix if entries in its
rows and columns are non-decreasing when moving towards the diagonal. A
Robinson similarity matrix can be viewed as the affinity matrix between objects
arranged in linear order, where objects closer together have higher affinity.
We define a new parameter, $\Gamma_\max$, which measures how badly a given
matrix fails to be Robinson similarity. Namely, a matrix is Robinson similarity
precisely when its $\Gamma_\max$ attains zero, and a matrix with small
$\Gamma_\max$ is close (in the normalized $\ell^1$-norm) to a Robinson
similarity matrix. Moreover, both $\Gamma_\max$ and the Robinson similarity
approximation can be computed in polynomial time. Thus, our parameter
recognizes Robinson similarity matrices which are perturbed by noise, and can
therefore be a useful tool in the problem of seriation of noisy data.
