My primary interest is the development and analysis of algorithms, particularly those that have practical applications. These practical applications have included plant breeding, motion planning, shape comparison, sensing, mesh generation, molecular matching, tools for analyzing/comparing protein shapes, and simulation of combustion. I have a strong record of cross-disciplinary research covering diverse application areas from computer vision to civil engineering to computational biology. I invented/discovered backwards analysis, a now-widely-used technique for the analysis of randomized algorithms.Many of the numerical techniques for solving partial differential equations (PDEs) require the creation of a mesh, a subdivision of the region-of-interest into simple shapes such as triangles or tetrahedra. Among other contributions to the field of mesh generation, I created one of the first mesh-generation algorithms to offer a mathematical guarantee about the quality of the resulting mesh. I introduced the concept now referred to as geometric spanners (I did not use this term in my original paper). In the plane, a geometric spanner is a graph such that, for each pair of vertices, the shortest path in the graph is within a constant factor of the straight-line Euclidean distance between the vertices. Spanners have been useful for proximity problems, motion planning, and telecommunication networks.In work for Nature Source Improved Plants, I developed and/or improved multiple algorithms related to plant breeding. Examples include SNP-calling for polyploid species, marker optimization (i.e., determining a marker subset that is well-distributed over the genome), genotype inference for multi-parent breeding populations, and efficient methods for marker imputation in breeding collections.In 2021, I received the SoCG (Symposium on Computational Geometry) Test of Time Award for my 1987 paper, Constrained Delaunay Triangulations. The award recognizes symposium papers with long term impact.