Manjanna, B2016-08-242023-10-202016-08-242023-10-202016ROLL NO. 11612315https://gyan.iitg.ac.in/handle/123456789/730Supervisor: Gautam Kumar DasMotivated by the applications in facility location, VLSI design, image processing and motion planning, geometric covering problems have been studied extensively in the literature. In this thesis various geometric covering problems such as covering points with disks, and squares, covering rectangular regions and convex polygonal regions with disks are considered. The problems are investigated by proposing approximation, parameterized and heuristic algorithms. The Discrete Unit Disk Cover (DUDC) problem is one of the well known geometric covering problems. The DUDC problem is a NP-complete problem.enMATHEMATICSThesis