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His research interests are in computational and combinatorial geometry and their applications. He has pioneered (with Jack Schwartz) the study of algorithmic motion planning in robotics during the early 1980s, and has been involved in many fundamental research studies that have helped to shape the fields of computational and combinatorial geometry. Among his major achievements, in addition to his earlier work on robotics, are the study of Davenport-Schinzel sequences and their numerous geometric applications, the study of geometric arrangements and their applications, efficient algorithms in geometric optimization (including the introduction and analysis of generalized linear programming), and the study of combinatorial problems involving point configurations, including, since 2008, the application of algebraic techniques to problems involving incidences, distinct and repeated distances, and other related problems in combinatorial and computational geometry.
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Discrete & Computational Geometrypp.1-44, (2024)
CoRR (2023): 67:1-67:14
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