Abstract
The point placement problem is to determine the locations of n distinct points on a line uniquely (up to translation and reflection) by making the fewest possible pairwise distance queries of an adversary. A number of deterministic and randomized algorithms are available when distances are known exactly. In this paper, we discuss the problem in an inexact model. This is when distances returned by the adversary are not exact; instead, only upper and lower bounds on the distances are provided. We propose an algorithm called DGPL for this problem that is based on a distance geometry approach that Havel [8] used to solve the molecular conformation problem. Our algorithm does not address the problems of query choices and their minimization; these remain open. We have used our DGPL algorithm for the probe location problem in DNA mapping, where upper and lower bounds on distance between some pairs of probes are known. Experiments show the superior performance of our algorithm compared to that of an algorithm by Mumey [9] for the same problem.
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Kannan, K.K.V., Sarker, P.K., Turdaliev, A., Mukhopadhyay, A. (2016). Point Placement in an Inexact Model with Applications. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9786. Springer, Cham. https://doi.org/10.1007/978-3-319-42085-1_7
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