A network flow method for solving some inverse combinatorial optimization problems

Abstract

We consider a set of inverse combinatorial optimization problems including inverse problems of minimum spanning tree problem, assignment problem and shortest path tree problem, etc. We suggest a method to solve these problems which first uses optimality conditions to formulate the inverse problems as some linear programming problems, find their dual problems, and then construct suitable network models to convert the dual problems into maximum-weight circulation problems. By using this method, the class of inverse problems can be handled uniformly with a strongly polynomial complexity.