k-SAT (Boolean Satisfiability)
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Description
k-SAT restricts the boolean formula to CNF with (at most) k literals per clause
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), 3SAT, 3SAT-5, 4SAT, Monotone 3SAT, XOR-SAT, Horn SAT, Dual-Horn SAT, Renamable Horn, MaxSAT
Parameters
$n$: number of variables
$k$: max number of literals per clause
$c$: dependant on $k$
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Paturi, Pudlák, Saks, Zane (PPSZ) | 2005 | O^*({2}^{n-cn/k}) | $O(kn)$ | Exact | Randomized | Time |
Reductions TO Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Subset Sum | assume: SETH then: for any $\epsilon > {0}$ there exists a $\delta > {0}$ such that Subset Sum is not in time $O(T^{1-\epsilon}{2}^{\delta n})$, and $k$-Sum is not in time $O(T^{1-\epsilon}n^{\delta k})$ |
2022 | https://dl.acm.org/doi/full/10.1145/3450524 | link |