Abstract
The concept of perfect phylogeny is observed to be non-universal, however, in some studies, it is shown that it provides great insights from a biological standpoint. Most natural phylogenies are imperfect but this is debated by the presence of noise in data acting as a disguise, the solution to uncover the underlying perfect phylogeny in the simplest approach is known as Minimum Character Removal (MCR) problem. Another variant of the solution achieved by a change in perspective and computational methodology is known as Maximal Character Compatibility (MCC) problem. Both MCR and MCC problems are solved optimally with reasonable efficiency by using Integer Linear Programming (ILP) technique. A central part of MCC solution involves solving the Max-clique problem of the generated representation allowing numerous clique-solving algorithms to generate various solutions. The comparison between the solution’s optimality and the run-time of these methods substantiates the goal of the different algorithms being applied. The above methods are formulated and implemented using modern programming languages like Python and Matlab. This exploration introduces the problem of perfect phylogeny, its ILP formulations, and its solution along with comparisons between different methods in consideration.
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References
Kanz, C., et al.: The EMBL nucleotide sequence database. Nucleic Acids Res. 33, D29–D33 (2005). ISSN 0305-1048. https://doi.org/10.1093/nar/gki098, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC540052/. Accessed 01 Dec 2022
Clark, K., et al.: GenBank. Nucleic Acids Res. 44, pp. D67–D72 (2016). ISSN 0305-1048. https://doi.org/10.1093/nar/gkv1276, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4702903/. Accessed 01 Dec 2022
NCBI Geo: archive for functional genomics data sets—update—Nucleic Acids Research—Oxford Academic. https://academic.oup.com/nar/article/41/D1/D991/1067995. Accessed 01 Dec 2022
miRBase: microRNA sequences, targets and gene nomenclature. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1347474/. Accessed 01 Dec 2022
Zou, D., et al.: Biological databases for human research. Genom. Proteomics Bioinform. 13(1), 55–63 (2015). ISSN 1672-0229. https://doi.org/10.1016/j.gpb.2015.01.006, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4411498/. Accessed 01 Nov 2022
Wang, Y.-X., Zhang, Y.-J.: Nonnegative matrix factorization: a comprehensive review. IEEE Trans. Knowl. Data Eng. 25(6), 1336–1353 (2013). https://doi.org/10.1109/TKDE.2012.51
Habib, M., Stacho, J.: Unique perfect phylogeny is intractable. Theoret. Comput. Sci. 476, 47–66 (2013)
Gusfield, D.: Integer Linear Programming in Computational and Systems Biology: An Entry-Level Text and Course. Cambridge University Press, Cambridge (2019). https://doi.org/10.1017/9781108377737
Anbuudayasankar, S., Mohandas, K.: Mixed-integer linear programming for vehicle routing problem with simultaneous delivery and PickUp with maximum route-length. Undefined (2008)
Kesav, R.S., Premjith, B., Soman, K.P.: Dependency parser for Hindi using integer linear programming. In: Singh, M., Tyagi, V., Gupta, P.K., Flusser, J., Ören, T., Sonawane, V.R. (eds.) ICACDS 2021. CCIS, vol. 1441, pp. 42–51. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88244-0_5. ISBN 978-3-030-88243-3
Nayak, S.: Chapter eight - integer programming. In: Nayak, S. (ed.) Fundamentals of Optimization Techniques with Algorithms, pp. 223–252. Academic Press (2020). ISBN 978-0-12-821126-7. https://doi.org/10.1016/B978-0-12-821126-7.00008-5, https://www.sciencedirect.com/science/article/pii/B9780128211267000085. Accessed 08 June 2022
Aparnna, T., Raji, P.G., Soman, K.P.: Integer linear programming approach to dependency parsing for MALAYALAM. In: 2010 International Conference on Recent Trends in Information, Telecommunication and Computing, pp. 324–326 (2010). https://doi.org/10.1109/ITC.2010.97
Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, pp. 1–74. Springer, Boston (1999). https://doi.org/10.1007/978-1-4757-3023-4_1
Belachew, M.T.: NMF-based algorithms for data mining and analysis: feature extraction, clustering, and maximum clique finding. Ph.D thesis (2014)
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Pranav Kumaar, B.E., Aadharsh Aadhithya, A., Sachin Kumar, S., Anandaram, H., Soman, K.P. (2023). Optimal Perfect Phylogeny Using ILP and Continuous Approximations. In: Singh, M., Tyagi, V., Gupta, P., Flusser, J., Ören, T. (eds) Advances in Computing and Data Sciences. ICACDS 2023. Communications in Computer and Information Science, vol 1848. Springer, Cham. https://doi.org/10.1007/978-3-031-37940-6_11
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