A PTAS for the Horizontal Rectangle Stabbing Problem

Arindam Khan, Aditya Subramanian, Andreas Wiese

Abstract: We study rectangle stabbing problems in which we are given n axis-aligned rectangles in the plane that we want to stab, i.e., we want to select line segments such that for each given rectangle there is a line segment that intersects two opposite edges of it. In the horizontal rectangle stabbing problem (Stabbing), the goal is to find a set of horizontal line segments of minimum total length such that all rectangles are stabbed. In general rectangle stabbing problem, also known as horizontal-vertical stabbing problem (HV-Stabbing), the goal is to find a set of rectilinear (i.e., either vertical or horizontal) line segments of minimum total length such that all rectangles are stabbed. Both variants are NP-hard. Chan, van Dijk, Fleszar, Spoerhase, and Wolff [5] initiated the study of these problems by providing O(1)-approximation algorithms. Recently, Eisenbrand, Gallato, Svensson, and Venzin [11] have presented a QPTAS and a polynomial-time 8-approximation algorithm for Stabbing but it is open whether the problem admits a PTAS.

External IDs:dblp:conf/ipco/KhanSW22