We present algorithms for the perfect phylogeny problem restricted to binary characters. The first algorithm is faster than a previous algorithm by Gusfield when the input matrix for the problem is sparse. Next, we present two online algorithms. For the first of these, the characters are given as input one at a time, while, for the second, the species are given as input one at a time. These two online algorithms can easily be combined into an algorithm that can process any sequence of additions and deletions of species and characters.