NP-Completeness of deciding the feasibility of Linear Equations over binary-variables with coefficients and constants that are 0, 1, or -1
Abstract
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is feasible, if and only if, the NP-Complete problem has a feasible solution. We show separate polynomial-time conversions to S, from the SUBSET-SUM and 3-SAT problems, both of which are NP-Complete. The number of equations and variables in S is bounded by a polynomial function of the size of the NP-Complete problem, showing that deciding the feasibility of S is strongly-NP-Complete. We also show how to apply the approach used for the SUBSET-SUM problem to decide the feasibility of Integer Linear Programs, as it involves reducing the coefficient-magnitudes of variables to the logarithm of their initial values, though the number of variables and equations are increased.
Keywords
Cite
@article{arxiv.1210.4120,
title = {NP-Completeness of deciding the feasibility of Linear Equations over binary-variables with coefficients and constants that are 0, 1, or -1},
author = {Deepak Ponvel Chermakani},
journal= {arXiv preprint arXiv:1210.4120},
year = {2012}
}
Comments
Proving strong NP-Completeness of our problem. Included a polynomial-time reduction from the 3-SAT problem