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Questions tagged [polynomial-time-reductions]

Used in questions asking for efficient (polynomial-time) reductions between computational problems.

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1 vote
3 answers
244 views

Spanning tree whose sum of edge weights are between two boundries

I saw this problem: $\langle G,w,k_1,k_2 \rangle \in L$ iff Graph $G$ has a spanning tree whose sum of edge wights are less than $k_2$ and greater than $k_1$. The problem says that we can prove this ...
Omid Yaghoubi's user avatar
2 votes
1 answer
211 views

Reduction from vertex-cover to system of quadratic equations

Define $$\text{SQE}=\{S\ |\ S\ \text{is a system of quadratic equations with real solutions}\}$$ and $$\text{VC}=\{G\ |\ G\ \text{is a simple undirected graph with a vertex cover}\ \leq k\}$$ I am ...
Tom Finet's user avatar
  • 258
2 votes
1 answer
42 views

Partition a family of sets to maximize cumulative overlap and cardinality

My problem is this: I have a list of $n$ items $N$ (think of them as the natural numbers $1,\dots,n$) and $m$ subsets of $N$ $S_1,\dots,S_m$ which may overlap. The objective is to find a partition of ...
Jonas Juul Hansen's user avatar
1 vote
1 answer
91 views

polynomial reduction within Np

If $A \le_p B$ and $B\in NP$, does it necessarily follow that $A\in NP$? ($\le_p$ is a polynomial many-one reduction) A quick yes/no comment is enough, a proof would be nice :-)
Jonas De Schouwer's user avatar
0 votes
0 answers
257 views

Horn Satisfiability is NP Complete, isn't it?

To show that any formal language is NP Complete first it must be showed that this formal language is both in NP and NP Hard. So to show that Horn Satisfiability is NP Complete first it must be showed ...
Farewell Stack Exchange's user avatar
0 votes
0 answers
32 views

computation P=L [duplicate]

i have the following question which I'm having some hard time to solve: prove: if every two Languages $A$ and $B$ that have a polynomial reduction ($A$ to $B$) also have a log space reduction ($A$ to ...
Nadav Shani's user avatar
0 votes
1 answer
160 views

Restriction of SAT to CNF

I have spent a lot of time understanding these two issues. If you can help me, please. Prove that the restriction of SAT to CNF formulas in which each variable xi appears at most twice is solvable in ...
tala's user avatar
  • 85