Abstract
The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.
Highlights
The binary linear programming (BLP) model is NP-complete and up to now we have not been aware of any polynomial algorithm for this model
In this paper we present a technique for transforming the BLP model into a convex quadratic programming (QP) problem
If any BLP can be converted into a convex quadratic problem, any BLP can be solved in polynomial time
Summary
The binary linear programming (BLP) model is NP-complete and up to now we have not been aware of any polynomial algorithm for this model. See for example Fortnow [1] [2] for more on complexity. In this paper we present a technique for transforming the BLP model into a convex quadratic programming (QP) problem. The optimal solution of the resultant convex QP is the optimal solution of the original problem BLP. This solves one of the famous open problems of whether P = NP or not
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