ON HITTING GRID POINTS IN A CONVEX POLYGON WITH STRAIGHT-LINES

Abstract

We consider the following problem: Find a set of parallel straight lines with equal spacing to hit all m grid points in a dosed region bounded by a convex polygon P with n vertices such that no grid points in a plane fall between two adjacent lines of these parallel lines and size of this set is minimal. We use continued fraction expansions to explore the combinatorial properties of this problem and propose an O(n + logm) approximation algorithm which guarantees finite performance ratio.