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The incomplete perfect phylogeny (IPP) problem and the incomplete perfect phylogeny haplotyping (IPPH) problem deal with constructing a phylogeny for a given set of haplotypes or genotypes with missing entries. The earlier approaches for both of these problems dealt with restricted versions of the problems, where the root is either available or can be trivially reconstructed from the data, or certain assumptions were made about the data. In this paper, we deal with the unrestricted versions of the problems, where the root of the phylogeny is neither available nor trivially recoverable from the data. Both IPP and IPPH problems have previously been proven to be NP-complete. Here, we present efficient enumerative algorithms that can handle practical instances of the problem. Empirical analysis on simulated data shows that the algorithms perform very well both in terms of speed and in terms accuracy of the recovered data.