Abstract
The point placement problem is to determine the positions of a set of n distinct points, P = {p 1, p 2, p 3, …, p n }, on a line uniquely, up to translation and reflection, from the fewest possible distance queries between pairs of points. Each distance query corresponds to an edge in a graph, called point placement graph (ppg), whose vertex set is P. The uniqueness requirement of the placement translates to line rigidity of the ppg. In this paper, we show how to construct in 2 rounds a line rigid ppg of size 9n/7 + O(1). This improves the best known result of 4n/3 + O(1). We also improve the lower bound on 2-round algorithms from 14n/13 to 9n/8.
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Alam, M.S., Mukhopadhyay, A. (2015). Three Paths to Point Placement. In: Ganguly, S., Krishnamurti, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2015. Lecture Notes in Computer Science, vol 8959. Springer, Cham. https://doi.org/10.1007/978-3-319-14974-5_4
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DOI: https://doi.org/10.1007/978-3-319-14974-5_4
Publisher Name: Springer, Cham
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