Top-k queries arise naturally in many database applications that require searching for records whose attribute values are close to those specified in a query. In this paper, we study the problem of processing a top-k query by translating it into an approximate range query that can be efficiently processed by traditional relational DBMSs. We propose a sampling-based approach, along with various query mapping strategies, to determine a range query that yields high recall with low access cost.Our experiments on real-world datasets show that, given the same memory budgets, our sampling-based estimator outperforms a previous histogram-based method in terms of access cost, while achieving the same level of recall. Furthermore, unlike the histogram-based approach, our sampling-based query mapping scheme scales well for high-dimensional data and is easy to implement with low maintenance cost.