Philip Klein does research in algorithms and data structures, especially in the area of combinatorial optimization, and especially those problems involving graphs. Past work includes approximation algorithms (including the development of the primal-dual method for the Steiner forest problem), randomized algorithms (including the first linear-time algorithm for finding minimum-cost spanning trees), and parallel algorithms (including the first linear-processor, polylog-time algorithms for fundamental problems in planar graphs, e.g. topological sorting and shortest paths). Recent work focuses on optimization problems in planar graphs, such as finding an approximately minimum-cost traveling salesperson tour in an undirected planar graph and finding a maximum st-flow in a directed planar graph.