The linear assignment problem (LAP) and linear bottleneck assignment problem (LBAP) has been unknown the algorithm to solve the optimal solution within polynomial-time. These problems are classified by NP-hard. Therefore, we can be apply metaheuristic...
The linear assignment problem (LAP) and linear bottleneck assignment problem (LBAP) has been unknown the algorithm to solve the optimal solution within polynomial-time. These problems are classified by NP-hard. Therefore, we can be apply metaheuristic methods or linear programming (LP) software package or Hungarian algorithm (HA) with O(m<sup>4</sup>) computational complexity. This paper suggests polynomial time algorithm with O(mn)=O(m<sup>2</sup>),m=n time complexity to LAP and LBAP. The select-delete method is simply applied to LAP, and the delete-select method is used to LBAP. For the experimental data without the unique algorithm can be apply to whole data, the proposed algorithm can be obtain the optimal solutions for whole data.