(Lethbridge, Alta : University of Lethbridge, Dept. of Mathematics and Computer Science, 2015) Jahan, Kawsar; University of Lethbridge. Faculty of Arts and Science; Gaur, Daya; Benkoczi, Robert
In this thesis, we study the problem of covering points with axis parallel lines. We named
it as the point cover problem. Given a set of the n points in d dimensional space, the goal
is to cover the points with minimum number of axis parallel lines. We use the iterative
rounding approach which gives an integral solution to the problem. We also propose a
combinatorial algorithm by using the branch and bound technique which gives an optimal
integral solution to the point cover problem. Later we implemented another approximation
algorithm based on primal-dual and iterative rounding approaches. Finally we show the
comparative analysis between the two iterative rounding algorithms.