Professor Naomi Nishimura's research is in the area of algorithms and complexity, with an emphasis on graph algorithms. Her main research interests involve the identification and use of structure in developing algorithms, such as graph algorithms, fixed-parameter algorithms, and algorithms for reconfiguration problems.
Parameterized complexity allows the development of efficient algorithms for various problems which, when considered in full generality, are considered to be intractable. The aim of the parameterized approach is to identify the source of complexity as one or more parameters of the problem, obtaining algorithms that are polynomial in the size of the input but possibly exponential in the parameter(s). In situations in which the parameters are guaranteed to be small in comparison to the size of the input, these techniques yield polynomial-time algorithms. Professor Nishimura's work includes the first parameterized algorithms for graph drawing problems and for backdoor sets for formulas for the satisfiability problem.
Reconfiguration considers the solution space of an instance of a problem, asking, for example, whether it is possible to transform one feasible solution into another in a sequence of reconfiguration steps such that each step results in a feasible solution. Professor Nishimura and her collaborators were the first to consider the parameterized complexity of reconfiguration problems, and continue to explore the two areas both singly and in combination. This work applies to a large range of problem domains, and is part of a long-term project to study algorithms for situations subject to change.