Probability of unique integer solution to a system of linear equations

European Journal of Operational Research

Volumn 214, Issue 1, 2011, Pages 27-30

  Mangasarian, O L ^a,b   Recht, Benjamin ^a  

^a University of Wisconsin Madison   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Linear equations; Linear programming; Unique integer solution

Indexed keywords

EMPIRICAL PERFORMANCE; INTEGER SOLUTIONS; LINEAR PROGRAMMING FORMULATION; LINEAR PROGRAMS; PRIMAL OPTIMAL SOLUTIONS; SUFFICIENT CONDITIONS; SYSTEM OF LINEAR EQUATIONS; UNIQUE INTEGER SOLUTION;

LINEAR EQUATIONS; LINEAR PROGRAMMING;

INTEGER PROGRAMMING;

EID: 79957973524     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2011.04.010     Document Type: Article

References (18)

1. G. Appa On the uniqueness of solutions to linear programs Journal of the Operational Research Society 53 2002 1127 1132
2. E.J. Cands, J. Romberg, and T. Tao Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information IEEE Transactions on Information Theory 52 2 2006 489 509 (Pubitemid 43174093)
3. David L. Donoho, and Jared Tanner Counting the faces of randomly-projected hypercubes and orthants with applications Discrete and Computational Geometry 43 3 2010 522 541
4. D. Fayard, and G. Plateau An algorithm for the solution of the 0-1 Knapsack problem Computing 28 1982 269 287 (Pubitemid 12550760)
5. J.J. Fuchs On sparse representations in arbitrary redundant bases IEEE Transactions on Information Theory 50 2004 1341 1344
6. W. Hoeffding Probability inequalities for sums of bounded random variables Journal of the American Statistical Association 58 301 1963 13 30
7. R. Horst, P. Pardalos, and N.V. Thoai Introduction to Global Optimization 1995 Kluwer Academic Publishers. Dodrecht, Netherlands
8. ILOG, Incline Village, Nevada. ILOG CPLEX 9.0 User's Manual, 2003. .
9. O.L. Mangasarian Uniqueness of solution in linear programming Linear Algebra and Its Applications 25 1979 151 162
10. O.L. Mangasarian Nonlinear Programming 1994 SIAM Philadelphia, PA
11. O.L. Mangasarian, Knapsack feasibility as an absolute value equation solvable by successive linear programming. Optimization Letters, 3:161-170, 2009. . Optimization Letters online version: .
12. O.L. Mangasarian, M.C. Ferris, Uniqueness of integer solution of linear equations. Technica6C Report 09-01, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, July 2009. . Optimization Letters 4, 2010, pp. 559-565.
13. MATLAB. User's Guide. The MathWorks, Inc.; Natick, MA 01760, 1994-2006. .
14. C.H. Papadimitriou On the complexity of unique solution Proceedings of the 23rd Annual Symposium on Foundations of Computer Science 1982 IEEE CNF Chicago, IL 14 20
15. O.A. Prokopyev, H.-X. Huang, and P.M. Pardalos On complexity of unconstrained hyperbolic 0-1 programming problems Operations Research Letters 33 2005 312 318
16. J. Rohn A theorem of the alternatives for the equation Ax + Bx = b Linear and Multilinear Algebra 52 6 2004 421 426
17. L.G. Valiant, and V.V. Vazirani Np is as easy as detecting unique solutions Annual ACM Symposium on Theory of Computing, Proceedings of the 17th Annual ACM Symposium on Theory of Computing 1985 Association for Computing Machinery New York, NY 458 463
18. J.G. Wendel A problem in geometric probability Mathematica Scandinavica 11 1962 109 111