Integer programing is one of the most narutal optimization tools.As an analogy of DNF or CNF in the Boolean function theory, we can consider the following equation.$x_{1}x_{2}x_{3}+$ $x_{3}x_{4}x_{5}+x_{1}x_{7}x_{9}=8,x_{i}\in \{0,1\}$This constraint is not a linear one. However, every variables in any monomial has at most degree $1$.Call constraints of this kind $multi$-$lienar$ constraints.We consider the following example as a instance of Multi-linear Integer($0$-$1$) programming, which is a system of multi-linear constraints. $5x_{1}x_{2}x_{3}+2x_{3}x_{4}x_{5}+x_{1}x_{7}x_{9}=8$$11x_{1}x_{3}+3x_{2}x_{4}x_{6}+23x_{3}x_{7}x_{8}+x_{10}=4$$x_{2}x_{6}+4x_{3}x_{4}x_{5}+5x_{5}x_{7}x_{9}=4$$x_{i} \in \{0,1\} $Where all coefficients of each monomial is integer and polynomial order $n^{O(1)}$($n$ is the number of variables)Solving Multi-linear 0-1 programming is deciding whether there exists an $0$-$1$ assingment which satisfies all of given multilinear constraints.Ofcourse $0-1$ programming is a $NP$-complete problem in one of the 21 problems which R.Karp showed their completeness. More over Exponential Time Hypothesis seems to  get rid of our hope to construct better sub-exponential time algorithms.My question is :QAre there any $slightly$ better exponential algorithm for Multi-linear 0-1 programming such as $2^{n-C\log n}$ time, $2^{n-C\log ^{2} n}$ times, or $2^{n-Cn^{0.001}}$ ?($C$ is a constant) ,and are there  text-books or papers contains algorithms for integer programming of this type ?
Slightly Faster Exponential Algorithm for Integer Programming with Multi-linear Variables
reference request;np hardness;optimization;integer programming;exp time algorithms