Mounts's main area of research is computational geometry, which is the branch of algorithms devoted to solving problems of a geometric nature.

Mount has worked on developing practical algorithms for k-means clustering, a problem known to be NP-hard.

By allowing the algorithm to return an approximate solution to the nearest neighbor query, a significant speedup in space and time complexity can be obtained.

, and forms a data structure that can be stored efficiently (low space complexity) and that returns the

In co-authored work with Arya, Netanyahu, R. Silverman and A. Wu,[3] Mount showed that the approximate nearest neighbor problem could be solved efficiently in spaces of low dimension.

The data structure described in that paper formed the basis of the ANN open-source library for approximate nearest neighbor searching.

Mount has also worked on point location, which involves preprocessing a planar polygonal subdivision S of size

space that when asked what cell a query point lies in, takes expected time

In addition to the design and analysis of algorithms in computational geometry, Mount has worked on the implementation of efficient algorithms in software libraries such as: As of December 8, 2009, here is a list of his most cited works (according to Google Scholar) and their main contributions, listed in decreasing order of citations: Mount was named to the 2022 class of ACM Fellows, "for contributions to algorithms and data structures for geometric data analysis and retrieval".