In optimal layout problems, which are often demanded by many industries, it is desired to have new computer-based approaches that are fast and effective. To determine the overall speed of layout procedure, one has to consider not only the search algorithm but also the performance of overlap detection algorithm. In this paper, a new methodology of detecting an overlap in two-dimensional layout problem is presented. This method introduces the concept of Minkowski sum, which is defined as an algebraic sum of two point sets, to the overlap detection. Using mathematical relations, the algorithm can rapidly detect if two convex objects are overlapping, fully contained or separated. Fast detection of overlaps eventually allows user to accelerate the overall speed of layout algorithms. In addition, to obtain the robustness of this method it is being extended to the cases involving irregular-shaped non-convex objects.