Computer Science Stack Exchange
Computer Science Stack Exchange

Questions tagged [np-hard]

decision problems that are at least as hard as NP-complete problems

NP-hard problems are NP-complete and harder problems. More precisely, a decision problem $H$ is NP-hard if there is another problem $H'$ that is NP-complete that can be reduced in polynomial time to $H$, i.e. solving $H$ leads to a solution for $H'$.

See also ,

847 questions
7
votes
2 answers

Is finding the smallest collection of subsets so that the number of elements among the subsets is <= the number of subsets NP-hard?

Given a collection of non-empty subsets of $\{1,2,\ldots,N\}$ ($N$ not fixed), the problem is to find the smallest non-empty collection of subsets so that the number of distinct elements appearing among the union of subsets is less than or equal to…
user2566092
  • 1,721
  • 10
  • 17
4
votes
1 answer

Are "pipes" puzzles NP-hard?

Is the decision version (i.e. does a solution exist) of this puzzle NP-hard (for an nxn puzzle)? It feels like it has very local strategies which allow easily solving the instances, but it's not obvious to me that these generalize to larger puzzles.…
Davis Yoshida
  • 371
  • 1
  • 10
1
vote
2 answers

Select the maximum number of links to satisfy the constraint on each link. How to prove is NP-hard?

Instance: $n$ non-negative real numbers $P_1,\ldots,P_n$, a positive number $k\le n$, and a positive number $\epsilon$. Question: Is there a subset $S$ of $\{1,\ldots,n\}$ of cardinality $|S|\geq k$ such that $$\dfrac{P_i}{\epsilon-P_i+\sum_{j\in…
Chiba
  • 17
  • 4
1
vote
1 answer

Prove L is NP-hard

I have no clue how to prove this question. Consider the language $L = \{ \langle D_1, D_2, ... ,D_K \rangle : k \in {N},$ the $D_i$ are DFAs and ${\bigcap}_{i=1}^k L(D_i) = \emptyset \}$ Prove that L is NP-hard. Can someone guide me through this…
vanblaze
  • 11
  • 1
1
vote
0 answers

Extended venn diagram

I try to solve a computational problem, but its solution lives on a generalized Venn diagram statement. I was able to obtain its general formula, but now I require some necessary conditions to avoid k combinations evaluation of intersection between…
Bruno Lobo
  • 123
  • 4
1
vote
1 answer

SImple NP-hard proof question

$3SATplus$ Input: 2 CNF formulas $F_1$, $F_2$ where all clauses have exactly $3$ literals. Question: Does every truth assignment satisfy at-least as many $F_2$ clauses as $F_1$'s? Assume $3SATPLUS \in NP$ Prove $3SAT \leq_p$ $3SATplus$ The…
bob
  • 27
  • 4
0
votes
1 answer

Select the maximum number of links to satisfy per-link constraint. How to prove is NP-hard?

I asked, incorrectly, my previous question here. I would like to thank D.W. for his answer though. He answeres that the problem is polynomial time solvable. The thing is that the cited paper shows that it is NP-hard. So I corrected my question. But…
Chiba
  • 17
  • 4
0
votes
2 answers

NP-hardness and Turing reducibility

I understand that if $A$ is NP-hard, and $A \leq_{T} B$, then $B$ is NP-hard. Is the converse also true? So if $B$ is NP-hard, and $A \leq_{T} B$, then $A$ is NP-hard? Why (not)?
meikyu
  • 3
  • 1
0
votes
1 answer

Understanding the complexity class of a problem formulation

I'll keep the reasoning abstract. If I start from a mathematical formulation of a problem $A$ known to be $NP$-hard, I add a set of constraints which creates a problem $A'$. However, I do know that there exists some instance of the problem for which…
Daniele Cuomo
  • 121
  • 4