Linear and semi-assignment problems: A core oriented approach

A Linear Assignment Problem (LAP) with a dense cost matrix can be solved by first making this matrix sparse, i.e. the problem is solved on the core of the matrix. For a known LAP algorithm the paper gives the related modifications. Computational results show that the algorithm is then suited to solve large problems. A standard personal computer can solve problem instances up to size 2000 within about 75 seconds. Furthermore, the paper describes versions of the algorithm for non-square problems as well as for semi-assignment problems; computational results for problem instances up to size 2500 show again the success of the core oriented approach for assignment problems.