Optimal algorithm for a special point-labeling problem

Abstract

We investigate a special class of map labeling problem.Let P = {p1, p2,..., pn} be a set of point sites distributed on a 2D map.A label associated with each point is a axis-parallel rectangle of a constant height but of variable width.Here height of a label indicates the font size and width indicates the number of characters in that label.F or a point pi, its label contains the point pi at its top-left or bottom-left corner, and it does not obscure any other point in P.Width of the label for each point in P is known in advance.The objective is to label the maximum number of points on the map so that the placed labels are mutually nonoverlapping. W e first consider a simple model for this problem.Here, for each point pi, the corner specification (i.e., whether the point pi would appear at the top-left or bottom-left corner of the label) is known.W e formulate this problem as finding the maximum independent set of a chordal graph, and propose an O(nlogn) time algorithm for producing the optimal solution.If the corner specification of the points in P is not known, our algorithm is a 2-approximation algorithm.Next, we develop a good heuristic algorithm that is observed to produce optimal solutions for most of the randomly generated instances and for all the standard benchmarks available in [13].