Symmetries in Linear and Integer Programs
نویسندگان
چکیده
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution in the fixed point set of its symmetry group. Using this result, we develop an algorithm that allows for reducing the dimension of any linear program having a non-trivial group of symmetries.
منابع مشابه
Symmetries in Integer Programs
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show that any integer program on n variables having an alternating group An as a group of symmetries can be solved in linear time in the number of variables.
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