  We apply analytically Niedermayer's algorithm to the Edwards-Anderson model
on random graphs with arbitary degree distributions. The results for the
multicritical point on the Nishimori line are shown. The results are shown by
applying a criterion for spin models on the random graphs with arbitary degree
distributions. The application of Niedermayer's algorithm makes the size of the
Fortuin-Kasteleyn cluster small and shifts the percolation threshold. The
results for the $\pm J$ model and the Gaussian model are respectively shown.
  In the present article, it is respectively shown for the $\pm J$ model and
the Gaussian model that, by adjusting an introduced parameter for Niedermayer's
algorithm, the percolation threshold obtained in the present article agrees
with the location of the multicritical point. We naively estimate the locations
of the multicritical points for the $\pm J$ model and the Gaussian model on the
randam graphs with arbitary degree distributions.
