The problem of Haplotype Assembly is an essential step in human genome analysis. It is typically formalised as the Minimum Error Correction (MEC) problem which is NP-hard. MEC has been approached using heuristics, integer linear programming, and xedparameter tractability (FPT), including approaches whose runtime is exponential in the length of the DNA fragments obtained by the sequencing process. Technological improvements are currently increasing fragment length, which drastically elevates computational costs for such methods. We present pWhatsHap, a multi-core parallelisation of WhatsHap, a recent FPT optimal approach to MEC. WhatsHap moves complexity from fragment length to fragment overlap and is hence of particular interest when considering sequencing technology's current trends. pWhatsHap further improves the eciency in solving the MEC problem, as shown by experiments performed on datasets with high coverage.