Approximation algorithms for aligning points

Sergio Cabello, Marc van Kreveld
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
We study the problem of aligning horizontally, vertically, or diagonally, as many points as possible when each point is allowed to be placed anywhere in its own, given region. Different shapes of placement regions and different sets of alignment orientations are considered. More generally, we assume that a graph is given on the points, and only the alignments of points that are connected in the graph count. For the case of trees and planar graphs, we give approximation algorithms whose
more » ... thms whose performance depends upon the shape of the given regions and the set of orientations. When the orientations to consider are the ones given by the axes and the regions are axis-parallel rectangles, we obtain a polynomial time approximation scheme.
doi:10.1145/777793.777796 fatcat:smivbzv5v5dzdeijsuvmyrfl2m