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TR15-112 | 16th July 2015 15:09

#### Improved Algorithms for Sparse MAX-SAT and MAX-$k$-CSP

TR15-112
Authors: Ruiwen Chen, Rahul Santhanam
Publication: 16th July 2015 20:10
Keywords:

Abstract:

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.

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