Abstract
In this paper, we study the adaptive version of the point placement problem on a line, which is motivated by a DNA mapping problem. To identify the relative positions of n distinct points on a straight line, we are allowed to ask queries of pairwise distances of the points in rounds. The problem is to find the number of queries required to determine a unique solution for the positions of the points up to translation and reflection. We improved the bounds for several cases. We show that \(4n/3 + O(\sqrt{n})\) queries are sufficient for the case of two rounds while the best known result was 3n/2 queries. For unlimited number of rounds, the best result was 4n/3 queries. We obtain a much better result of using \(5n/4 + O(\sqrt{n})\) queries with three rounds only. We also improved the lower bound of 30n/29 to 17n/16 for the case of two rounds.
This research is supported by the RGC grant HKU7119/05E.
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References
Damaschke, P.: Point Placement on the Line by Distance Data. Discrete Applied Mathematics 127, 53–62 (2003)
Damaschke, P.: Randomized vs. Deterministic Distance Query Strategies for Point Location on the Line. Discrete Applied Mathematics 154, 478–484 (2006)
Mumey, B.: Probe Location in the Presence of Errors: A Problem from DNA Mapping. Discrete Applied Mathematics 104, 187–201 (2000)
Redstone, J., Ruzzo, W.L.: Algorithms for a Simple Point Placement Problem. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds.) CIAC 2000. LNCS, vol. 1767, pp. 32–43. Springer, Heidelberg (2000)
Trask, B.J., Allen, S., Massa, H., Fertitta, A., Sachs, R., Engh, G., Wu, M.: Studies of Metaphase and Interphase Chromosomes using Fluorescence in situ Hybridication. Cold Spring Harbor Symposia on Quantitative Biology LVIII, 767–775 (1993)
Waterman, M.S.: Introduction to Computational Biology. Maps, Sequences and Genomes. Chapman and Hall, London (1995)
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Chin, F.Y.L., Leung, H.C.M., Sung, W.K., Yiu, S.M. (2007). The Point Placement Problem on a Line – Improved Bounds for Pairwise Distance Queries. In: Giancarlo, R., Hannenhalli, S. (eds) Algorithms in Bioinformatics. WABI 2007. Lecture Notes in Computer Science(), vol 4645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74126-8_35
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DOI: https://doi.org/10.1007/978-3-540-74126-8_35
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