Shadow mapping is a fast and easy to use method to produce hard shadows. However, it introduces aliasing due to its uniform sampling strategy and limited shadow map resolution. In this paper, we propose a memory efficient algorithm to render high quality shadows. Our algorithm is based on a multi-resolution shadow map structure, which includes a conventional shadow map for scene regions where a low-resolution shadow map is sufficient, and a high-resolution patch buffer to capture scene regions that are susceptible to aliasing. With this data structure, we are able to capture shadow details with far less memory footprint than conventional shadow mapping. In order to maintain an appropriate performance compared to conventional shadow mapping, we designed a customized CUDA rasterizer to render the high-resolution patches.