|. If and ?. G. |l, |, then Eq. (66) gives L ? ?1 G,? (?(? )) \ ?[i ? 1] = ?. If |T | = |L ? ?1 G,? (?(? ))|, as we surely have, Eq. (66) leads to L ? ?1 G,? (?(? )) \ ?[i ? 1] = ?, as was to be shown

@. Compute-the and T. , u) ? ?[i ? 1] ? ?[? ? 1] and its size |T |. Determine which is true, this step can be done in O(deg G (?(i))) time

@. If, |. |l, and ?. G. , ? (?(? ))|, according to the Claim and our algorithm description, we should set ?(i) to be ?(? )

@. If, L. , and ?. G. , \ ?[i ? 1] = ?, according to the Claim and our algorithm description, we should proceed to check whether or not it holds f ? (w) > ? and this costs O(1) time. If f ? (w) > ? , we set ?(i) = w and else we set ?(i) = ?(? )

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