ON THE DISCRETE UNIT DISK COVER PROBLEM

Abstract

Given a set [Formula: see text] of n points and a set [Formula: see text] of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in [Formula: see text] is covered by at least one disk in [Formula: see text] or not and (ii) if so, then find a minimum cardinality subset [Formula: see text] such that the unit disks in [Formula: see text] cover all the points in [Formula: see text]. The discrete unit disk cover problem is a geometric version of the general set cover problem which is NP-hard. The general set cover problem is not approximable within [Formula: see text], for some constant c, but the DUDC problem was shown to admit a constant factor approximation. In this paper, we provide an algorithm with constant approximation factor 18. The running time of the proposed algorithm is [Formula: see text]. The previous best known tractable solution for the same problem was a 22-factor approximation algorithm with running time [Formula: see text].