MaxSAT

Description

Given an instance of SAT represented in Conjunctive Normal Form (CNF), compute an assignment to the variables that maximizes the number of satisfied clauses.

Related Problems

Generalizations: Conjunctive Normal Form SAT

Related: SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT), k-SAT, 2SAT, 3SAT, 3SAT-5, 4SAT, Monotone 3SAT, XOR-SAT, Horn SAT, Dual-Horn SAT, Renamable Horn

Parameters

$n$: number of variables

Table of Algorithms

Currently no algorithms in our database for the given problem.

Reductions TO Problem

Problem	Implication	Year	Citation	Reduction
st-Maximum Flow	assume: SETH then: for any fixed constants $\epsilon > {0}$, $c_1,c_2 \in ({0},{1})$, on graphs with $n$ nodes $|S|=\tilde{\Theta}(n^{c_1})$, $|T|=\tilde{\Theta(n^{c_2})}$, $m=O(n)$ edges, and capacaties in $\{1,\cdots,n\}$, target cannot be solved in $O((|S|T|m)^{1-\epsilon})$	2018	https://dl.acm.org/doi/abs/10.1145/3212510	link
All-Pairs Maximum Flow	assume: SETH then: for any fixed $\epsilon > {0}$, in graphs with $n$ nodes, $m=O(n)$ edges, and capacities in $\{1,\cdots,n\}$ target cannot be solved in time $O((n^{2}m)^{1-\epsilon})$	2018	https://dl.acm.org/doi/abs/10.1145/3212510	link
All-Pairs Maximum Flow	assume: SETH then: for any fixed constants $\epsilon > {0}$, $c_1,c_2 \in ({0},{1})$, on graphs with $n$ nodes $|S|=\tilde{\Theta}(n^{c_1})$, $|T|=\tilde{\Theta(n^{c_2})}$, $m=O(n)$ edges, and capacaties in $\{1,\cdots,n\}$, target cannot be solved in $O((|S|T|m)^{1-\epsilon})$	2018	https://dl.acm.org/doi/abs/10.1145/3212510	link
st-Maximum Flow	assume: SETH then: for any fixed $\epsilon > {0}$, in graphs with $n$ nodes, $m=O(n)$ edges, and capacities in $\{1,\cdots,n\}$ target cannot be solved in time $O((n^{2}m)^{1-\epsilon})$	2018	https://dl.acm.org/doi/abs/10.1145/3212510	link
Maximum Local Edge Connectivity	assume: SETH then: for any $\epsilon > {0}$, in graphs with $n$ nodes and $\tilde{O}(n)$ edges, target cannot be solved in time $O(n^{2-\epsilon})$	2018	https://dl.acm.org/doi/abs/10.1145/3212510	link