Generalized jewels and the point placement problem

The point placement problem is to determine the positions of a linear set of points, P = {p1, p2, p3, . . . , pn}, 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 10n/7+O(1) from small rigid components called 5:5 jewels, which are an extension of the 4:4 jewel of [2]. Though this result is slightly worse than the 4n/3 + O( n) upper bound, reported in [1], this is more than offset by the potential for generalization of this construction.

• Type: Conference
• Year: 2009
• Where: CCCG
• Authors: Md. Shafiul Alam, Asish Mukhopadhyay, Animesh Sarker
• Keywords: CCCG 2007, CCCG 2009, Fewest Possible Distance, Point Placement, Point Placement Problem