DNA read mapping is a ubiquitous task in bioinformatics, and many tools have been developed to solve the read mapping problem. However, there are two trends that are changing the landscape of readmapping: First, new sequencing technologies provide very long reads with high error rates (up to 15%). Second, many genetic variants in the population are known, so the reference genome is not considered as a single string over ACGT, but as a complex object containing these variants. Most existing read mappers do not handle these new circumstances appropriately. We introduce a new read mapper prototype called VATRAM that considers variants. It is based on Min-Hashing of q-gram sets of reference genome windows. Min-Hashing is one form of locality sensitive hashing. The variants are directly inserted into VATRAMs index which leads to a fast mapping process. Our results show that VATRAM achieves better precision and recall than state-of-the-art read mappers like BWA under certain cirumstances. VATRAM is open source and can be accessed at https://bitbucket.org/Quedenfeld/vatram-src/.