Abstract
In this paper we consider the problem of arranging segments on parallel arcs drawn within a circular sector, to provide foundational work for the visualization of genomic regions in the study of pathogenic integration. The arcs as well as the start and end angles for each segment are pre-defined; our problem is to place each segment on an arc without having them overlap. There are no segments that span multiple arcs. For visualization purpose, the segments are to be easily distinguishable. To achieve that we consider various criteria that in a sense, place segments as far as possible from each other—for instance, maximizing the sum of inter-center distances between nearest segments. We show complexity results for some of the resultant problems, while providing approximation or heuristic solutions for others. Our algorithms have been implemented in JavaScript and made available at https://github.com/kalngyk/segmentplacer.
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References
Adey, A., Burton, J.N., Kitzman, J.O., Hiatt, J.B., Lewis, A.P., Martin, B.K., Qiu, R., Lee, C., Shendure, J.: The haplotype-resolved genome and epigenome of the aneuploid hela cancer cell line. Nature 500(7461), 207–211 (2013)
Forment, J.V., Kaidi, A., Jackson, S.P.: Chromothripsis and cancer: causes and consequences of chromosome shattering. Nat. Rev. Cancer 12(10), 663 (2012)
Kataoka, K., Shiraishi, Y., Takeda, Y., Sakata, S., Matsumoto, M., Nagano, S., Maeda, T., Nagata, Y., Kitanaka, A., Mizuno, S., et al.: Aberrant PD-L1 expression through 3\(^{\prime }\)-UTR disruption in multiple cancers. Nature 534(7607), 402 (2016)
Kleinberg, J., Tardos, É.: Algorithm Design. Addison Wesley, Reading (2006)
Knuth, D.E.: Art of Computer Programming, Volume 1: Fundamental Algorithms. Addison-Wesley Professional, Reading (1973)
Li, S.C., Leong, H.W., Quek, S.K.: New approximation algorithms for some dynamic storage allocation problems. In: Chwa, K.-Y., Munro, J.I.J. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 339–348. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27798-9_37
Lipson, D., Capelletti, M., Yelensky, R., Otto, G., Parker, A., Jarosz, M., Curran, J.A., Balasubramanian, S., Bloom, T., Brennan, K.W., et al.: Identification of new ALK and RET gene fusions from colorectal and lung cancer biopsies. Nat. Med. 18(3), 382 (2012)
Nault, J.-C., Datta, S., Imbeaud, S., Franconi, A., Mallet, M., Couchy, G., Letouzé, E., Pilati, C., Verret, B., Blanc, J.-F., et al.: Recurrent AAV2-related insertional mutagenesis in human hepatocellular carcinomas. Nat. Genet. 47(10), 1187 (2015)
Robson, J.M.: Bounds for some functions concerning dynamic storage allocation. J. ACM 21(3), 491–499 (1974)
Soda, M., Choi, Y.L., Enomoto, M., Takada, S., Yamashita, Y., Ishikawa, S., Fujiwara, S., Watanabe, H., Kurashina, K., Hatanaka, H., et al.: Identification of the transforming EML4-ALK fusion gene in non-small-cell lung cancer. Nature 448(7153), 561 (2007)
Stephens, P.J., McBride, D.J., Lin, M.-L., Varela, I., Pleasance, E.D., Simpson, J.T., Stebbings, L.A., Leroy, C., Edkins, S., Mudie, L.J., et al.: Complex landscapes of somatic rearrangement in human breast cancer genomes. Nature 462(7276), 1005 (2009)
Sung, W.-K., Zheng, H., Li, S., Chen, R., Liu, X., Li, Y., Lee, N.P., Lee, W.H., Ariyaratne, P.N., Tennakoon, C., et al.: Genome-wide survey of recurrent HBV integration in hepatocellular carcinoma. Nat. Genet. 44(7), 765–769 (2012)
Waddell, N., Pajic, M., Patch, A.-M., Chang, D.K., Kassahn, K.S., Bailey, P., Johns, A.L., Miller, D., Nones, K., Quek, K., et al.: Whole genomes redefine the mutational landscape of pancreatic cancer. Nature 518(7540), 495 (2015)
Yang, L., Luquette, L.J., Gehlenborg, N., Xi, R., Haseley, P.S., Hsieh, C.-H., Zhang, C., Ren, X., Protopopov, A., Chin, L., et al.: Diverse mechanisms of somatic structural variations in human cancer genomes. Cell 153(4), 919–929 (2013)
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Ng, Y.K., Jia, W., Li, S.C. (2018). Placing Segments on Parallel Arcs. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_25
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DOI: https://doi.org/10.1007/978-3-319-94667-2_25
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