TR15-112 Authors: Ruiwen Chen, Rahul Santhanam

Publication: 16th July 2015 20:10

Downloads: 1895

Keywords:

We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-$k$-CSP. For instances with $n$ variables and $cn$ clauses (constraints), we give algorithms running in time $\poly(n)\cdot 2^{n(1-\mu)}$ for

\begin{itemize}

\item $\mu = \Omega(\frac{1}{c} )$ and polynomial space solving MAX-SAT and MAX-$k$-SAT,

\item $\mu = \Omega(\frac{1}{\sqrt{c}} )$ and exponential space solving MAX-SAT and MAX-$k$-SAT,

\item $\mu = \Omega(\frac{1}{ck^2} )$ and polynomial space solving MAX-$k$-CSP,

\item $\mu = \Omega(\frac{1}{\sqrt{ck^3}} )$ and exponential space solving MAX-$k$-CSP.

\end{itemize}

The previous MAX-SAT algorithms have savings $\mu=\Omega(\frac{1}{c^2 \log^2 c})$ for running in polynomial space~\cite{SST14} and $\mu=\Omega(\frac{1}{c \log c})$ for exponential space~\cite{DW06}. We also give an algorithm with improved savings for satisfiability of depth-2 threshold circuits with $cn$ wires.