A new algorithm and improved lower bound for point placement on a line in two rounds

In this paper we show how to construct in 2 rounds a line-rigid point placement graph of size 4n/3+O(1) from small graphs called 6:6 jewels, an extension of the 4:4 jewel of [3]. This improves a result reported in [2] that uses 5-cycles. More significantly, we improve their lower bound on 2-round algorithms from 17n/16 to 14n/13.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Md. Shafiul Alam, Asish Mukhopadhyay
• Keywords: CCCG 2010, Computational Geometry, Lower Bound, Point Placement Graph, Small Graphs