For some types of integer programming problems,their LP relaxation solutions are optimal.

Name: For some types of integer programming problems,their LP relaxation solutions are optimal.
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For some types of integer programming problems, particularly those that are totally unimodular (where the determinant of every square submatrix is 0, 1, or -1), the solutions to their linear programming (LP) relaxations are integral and thus optimal for the original integer programming problem.

For Some Types of Integer Programming Problems,their LP Relaxation Solutions