Abstract
This paper proposes a strongly polynomial algorithm which either finds a solution of a linear system Ax = b, 0 ≤ x ≤ 1, or correctly decides that the system has no 0,1-solutions. The algorithm can be used as the basis for the construction of a polynomial algorithm for linear programming.
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References
Agmon Sh.: The relaxation method for linear inequalities. Can. J. Math. 6, 382–392 (1954)
Chubanov, S.: A polynomial relaxation-type algorithm for linear programming. http://www.optimization-online.org/DB_HTML/2011/02/2915.html (2010)
Edmonds J.: Systems of distinct representatives and linear algebra. J. Res. Nat. Bur. Standards 71B, 241–245 (1967)
Karmarkar N.: A new polynomial-time algorithm for linear programming. Combinatorica 4, 353–395 (1984)
Khachiyan, L.G.: A polynomial algorithm in linear programming. Dokl. Akad. Nauk SSSR 244 (English translation: Soviet Math. Dokl. 20, 191–194) (1979)
Motzkin Th., Schoenberg I.J.: The relaxation method for linear inequalities. Can. J. Math. 6, 393–404 (1954)
Tardos E.: A strongly polynomial algorithm to solve combinatorial linear programs. Oper. Res. 34, 250–256 (1986)
Todd M.: The many facets of linear programming. Math. Programm. 91, 417–436 (2002)
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Chubanov, S. A strongly polynomial algorithm for linear systems having a binary solution. Math. Program. 134, 533–570 (2012). https://doi.org/10.1007/s10107-011-0445-3
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DOI: https://doi.org/10.1007/s10107-011-0445-3