Discussion
Solution to the balanced assignment problem is binary due to :
Answer: D
The binary solution is due to the (totally) unimodular property.
The assignment constraints \(\sum_{j} x_{ij} = 1\), \(\sum_{i} x_{ij} = 1\) have a coefficient matrix that is totally unimodular: every square submatrix has determinant 0 or \(\pm 1\). With integer right-hand sides, every basic feasible solution of such a system is integral (by Cramer's rule), and with the bounds \(0 \le x_{ij} \le 1\) the vertices are 0-1 vectors. So solving the linear programming relaxation already gives a binary assignment.
A linear formulation alone does not give integrality, a non-empty feasible region only guarantees some solution, and the Hungarian method is an exact algorithm, not an approximate one.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development