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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 ,

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Why hasn't there been an encryption algorithm that is based on the known NP-Hard problems?

Most of today's encryption, such as the RSA, relies on the integer factorization, which is not believed to be a NP-hard problem, but it belongs to BQP, which makes it vulnerable to quantum computers. I wonder, why has there not been an encryption…
Ken Li
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Decision problems vs "real" problems that aren't yes-or-no

I read in many places that some problems are difficult to approximate (it is NP-hard to approximate them). But approximation is not a decision problem: the answer is a real number and not Yes or No. Also for each desired approximation factor,…
Ran G.
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Is it NP-hard to fill up bins with minimum moves?

There are $n$ bins and $m$ type of balls. The $i$th bin has labels $a_{i,j}$ for $1\leq j\leq m$, it is the expected number of balls of type $j$. You start with $b_j$ balls of type $j$. Each ball of type $j$ has weight $w_j$, and want to put the…
Chao Xu
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NP-Hard problems that are not in NP but decidable

I'm wondering if there is a good example for an easy to understand NP-Hard problem that is not NP-Complete and not undecidable? For example, the halting problem is NP-Hard, not NP-Complete, but is undecidable. I believe that this means that it is a…
oneself
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Selling blocks of time slots

Given $n$ time slots that $k$ people want to buy. Person $i$ has a value $h(i,j)\geq 0$ for each time slot $j$. Each person can only buy one consecutive block of time slots, which could be empty. Is there a polynomial-time algorithm to compute the…
user11550
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Is Dominosa NP-Hard?

Dominosa is a relatively new puzzle game. It is played on an $(n+1)\times(n+2)$ grid. Before the game begins, the domino bones $\left(0,0\right),\left(0,1\right),\ldots,\left(n,n\right)$ are placed on the grid (constituting a perfect tiling).…
Yoav bar sinai
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Reduce hitting set to SAT, and cardinality constraints

Here is the problem. Given $k, n, T_1, \ldots, T_m$, where each $T_i \subseteq \{1, \ldots, n\}$. Is there a subset $S \subseteq \{1, \ldots, n\}$ with size at most $k$ such that $S \cap T_i \neq \emptyset$ for all $i$? I am trying to reduce this…
Aden Dong
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Natural candidates for the hierarchy inside NPI

Let's assume that $\mathsf{P} \neq \mathsf{NP}$. $\mathsf{NPI}$ is the class of problems in $\mathsf{NP}$ which are neither in $\mathsf{P}$ nor in $\mathsf{NP}$-hard. You can find a list of problems conjectured to be $\mathsf{NPI}$ here. Ladner's…
Mohammad Al-Turkistany
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Is finding a weight-balanced tree NP-hard?

In the following, we consider binary trees where only the leaves have weights. Let $T$ be a binary tree and $W(T)$ be the sum of the weights of its leaves. Let $T.l$ and $T.r$ be the left child and right child respectively. We define the imbalance…
rex123
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Is every NP-hard problem computable?

Is it required that a NP-hard problem must be computable? I don't think so, but I am not sure.
Kevin Meier
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Proving that the conversion from CNF to DNF is NP-Hard

How can I prove that the conversion from CNF to DNF is NP-Hard? I'm not asking for an answer, just some suggestions about how to go about proving it.
jkjk
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Easy reduction from 3SAT to Hamiltonian path problem

There is a reduction in Sipser's book "Introduction to the theory of computation" on page 286 from 3SAT to Hamiltonian path problem. Is there a simpler reduction? By simpler I mean a reduction that would be easier to understand (for…
Kaveh
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Subset Sum: reduce special to general case

Wikipedia states the subset sum problem as finding a subset of a given multiset of integers, whose sum is zero. Further it states that it is equivalent to finding a subset with sum $s$ for any given $s$. So I believe as they are equivalent, there…
ipsec
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Is the following problem NP-hard? (or have you seen it before?)

I genuinely don't know if the following problem is NP-hard. I have never seen it mentioned online, but it's hard to even search for exact problems like this. I have been trying to find an efficient algorithm for a while and intuitively it feels very…
QuinnF
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Are "Flow Free" puzzles NP-hard?

A "Flow Free" puzzle consists of a positive integer $n$ and a set of (unordered) pairs of distinct vertices in the $n \times n$ grid graph such that each vertex is in at most one pair. A solution to such a puzzle is a set of undirected paths in the…
user12859
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