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Operations Research

The Operations Research area has two themes of primary focus: computational geometry, and stochastic optimization. The computational geometry group consists of Esther Arkin and Joe Mitchell along with adjunct faculty Michael Bender, Jie Gao, and Steve Skiena in Computer Science. The stochastic optimization group consists of Eugene Feinberg, Jiaqiao Hu, and Professor Zhenhua Liu, along with adjunct professors Ji Liu and Thomas Robertazzi in Electrical and Computer Engineering.  

Computational Geometry

Esther Arkin's primary research area is the design and analysis of algorithms that arise in network optimization, computational geometry, graph theory, scheduling, robotics, geographic information systems, computer graphics, manufacturing, and computer vision. Arkin is interested in theoretical analysis of worst-case complexity of problems, especially those that require optimization. She collaborates extensively with Joe Mitchell. For more information, see Arkin webpage. 

Joe Mitchell's primary research area is computational geometry, applied to pratical problems in computer graphics, visualization, robotics, manufacturing, geographic information systems, and computer vision. Mitchell is one of the country's leaders in computational geometry, which studies the design, analysis, and implementation of efficient algorithms to solve geometric problems; in the 1990's, he chaired the National Science Foundation advisory committee in computational geometry. A major current application is helping air traffic controllers route airplanes around storm systems as they approach an airport. For more information, see Mitchell webpage.

Stochastic Optimization
Eugene Feinberg works in stochastic methods of operations research and their industrial applications. He is one of the leaders in Markov decision processes and their application to telecommunication, manufacturing, transportation, service and to other man-made systems. He is also one of the country's experts on optimizing electric energy systems and forecasting energy demand. For more information, see Feinberg webpage.

Jiaqiao Hu's research is focused on designing and analyzing randomized algorithms for solving Markov decision processes and global optimization problems. He has been investigating new sampling and simulation-based techniques to overcome the computational difficulties associated with traditional methods, where sampling and simulation techniques are used not only to avoid enumerating the entire solution space but also to resolve the issue of the unavailability of explicit mathematical models of the underlying systems. For more information, see Hu webpage.

Other Research Interests
Zhenhua Liu's  current research interests include sustainable computing and networking systems, cloud platforms for big data applications and energy management, and renewable energy integration. He develops and applies techniques from distributed system, nonlinear optimization, game theory, and online algorithm for these systems. In particular, his research combines rigorous analysis and system design, and goes from theory, to prototype, and eventually to industry to make real impacts.  

Alan Tucker started his career at Stony Brook doing research in graph theory and combinatorial algorithms. Increasingly he  became more engaged in  mathematics education. He directed  large regional and national NSF initiatives to improve collegiate and K-12 mathematics instruction.  He was the lead author of four influential reports from the Mathematical Association of America, including  The Mathematical Education of Teachers (2001).