Lower bound of the filter ratio of area-maximizing points

In a spatial database and geographic information system (GIS), it is important to use a filter-refinement method to improve the performance of spatial query processing. The key factor to the filter-refinement method is employment of a highly efficient approximation. There are many kinds of established approximations but area-maximizing points (AMP) is suggested as an efficient and optimal point-based approximation with regards to the window query, which is one of the most important operations in a spatial database and GIS. This paper presents a lower bound of the filter ratio of AMP. The lower bound of the filter ratio of an approximation is very significant because it means the worst-case performance of the approximation. We show that the AMP shows the filter ratio greater than or equal to 0.5. This is the property that other approximations do not have.