Vera Traub conducts research at the interface between discrete mathematics and theoretical computer science in the field of combinatorial optimisation. This deals with issues where a particularly good solution is to be found from a large number of individually possible variants. In her dissertation, Traub worked on so-called approximation algorithms to solve the travelling salesman problem, a well-known problem in mathematics in which the shortest circular route between several cities is to be determined without trying out all the variants individually. This usually involves the use of certain algorithms. Traub found a new approach for this based on dynamic programming: her algorithm comes up with significantly better solutions in the same amount of time than previous algorithms are able to. In more recent work, she also deals with the design of networks. In this area, too, Traub has been able to develop new methods which are superior to all previously known methods.