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In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists a method to reduce a SAT (Satifiability) problem to Subset Sum Problem (SSP) in the literature, however, it can only be applied to small or medium size problems. Our study is to find an efficient method to transform a SAT problem to a mixed integer linear programming problem in larger size. Observing the feature of variable-clauses constraints in SAT, we apply linear inequality model (LIM) to the problem and propose a method called LIMSAT. The new method can work efficiently for very large size problem with thousands of variables and clauses in SAT tested using up-to-date benchmarks.
Recently a novel framework has been proposed for designing the molecular structure of chemical compounds using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). In the framework, we first define a feature vector $f(C
Many papers in the field of integer linear programming (ILP, for short) are devoted to problems of the type $max{c^top x colon A x = b,, x in mathbb{Z}^n_{geq 0}}$, where all the entries of $A,b,c$ are integer, parameterized by the number of rows of
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational burden witho
For a graph $G= (V,E)$, a double Roman dominating function (DRDF) is a function $f : V to {0,1,2,3}$ having the property that if $f (v) = 0$, then vertex $v$ must have at least two neighbors assigned $2$ under $f$ or {at least} one neighbor $u$ with
A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in polynomial t