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Parts of WhatsHap have been described in different articles. Please choose an appropriate citation depending on your use case.

If you use WhatsHap as a tool:

Marcel Martin, Murray Patterson, Shilpa Garg, Sarah O. Fischer, Nadia Pisanti, Gunnar W. Klau, Alexander Schoenhuth, Tobias Marschall.
WhatsHap: fast and accurate read-based phasing
bioRxiv 085050

To refer to the core WhatsHap phasing algorithm:

Murray Patterson, Tobias Marschall, Nadia Pisanti, Leo van Iersel, Leen Stougie, Gunnar W. Klau, Alexander Schönhuth.
WhatsHap: Weighted Haplotype Assembly for Future-Generation Sequencing Reads
Journal of Computational Biology, 22(6), pp. 498-509, 2015.

To refer to the pedigree-phasing algorithm and the PedMEC problem:

Shilpa Garg, Marcel Martin, Tobias Marschall.
Read-based phasing of related individuals
Bioinformatics 2016; 32 (12): i234-i242.

WhatsHap's genotyping algorithm is described here:

Jana Ebler, Marina Haukness, Trevor Pesout, Tobias Marschall, Benedict Paten.
Haplotype-aware genotyping from noisy long reads
bioRxiv

The HapChat algorithm is an alternative MEC solver able to handle higher coverages. It can be used through "whatshap phase --algorithm=hapchat". It has been described in this paper:

Stefano Beretta, Murray Patterson, Simone Zaccaria, Gianluca Della Vedova, Paola Bonizzoni.
HapCHAT: adaptive haplotype assembly for efficiently leveraging high coverage in long reads.
BMC Bioinformatics, 19:252, 2018.

A parallelization of the core dynamic programming algorithm (“pWhatsHap”) has been described in

M. Aldinucci, A. Bracciali, T. Marschall, M. Patterson, N. Pisanti, M. Torquati.
High-Performance Haplotype Assembly
Proceedings of the 11th International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics (CIBB), 245-258, 2015.

pWhatsHap is currently not integrated into the main WhatsHap source code. It is available in branch parallel in the Git repository.

If you use the polyploid phasing algorithm (whatshap polyphase), please refer to

Sven D. Schrinner, Rebecca Serra Mari, Jana Ebler, Mikko Rautiainen, Lancelot Seillier,
Julia J. Reimer, Björn Usadel, Tobias Marschall, Gunnar W. Klau.
Haplotype threading: accurate polyploid phasing from long reads
Genome Biology