Questions tagged [np-complete]

Questions about the hardest problems in NP, i.e. of those that can be solved in polynomial time by nondeterministic Turing machines.

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prove (iMC) i-Max-Clique is NPC

the iMC problem defined as follows: Given graph "G", natural numbers 'k' and 'i' in graph "G" exist 'i' disjointed cliques which are at size 'k'
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1answer
35 views

i-max-clique is np complete

How to prove the np completeness of the problem i-max-clique ? iMC is defined as follows: Given "i" number of cliques and "k" size of the clique, the graph will contain 'i' cliques at size 'k'
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0answers
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Proving NP-completeness of an extension in List Coloring Problem

In the List Coloring Problem (LCP), one is given an undirected graph $G(V,E)$, each vertex $v \in V$ is given a list of permissible colors $L(v) \subseteq \{1,2,\dots,k\}$, we want to find a coloring $...
12
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2answers
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Can any NP-Complete Problem be solved using at most polynomial space (but while using exponential time?)

I read about NPC and its relationship to PSPACE and I wish to know whether NPC problems can be deterministicly solved using an algorithm with worst case polynomial space requirement, but potentially ...
1
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1answer
22 views

Reducing 3 SAT to 3 SET PACKING

I'm trying to prove NP-hardness of 3 SET PACKING, which is a following problem: given a family of sets where each set contains 3 elements, decide whether the family contains k sets that are pairwise ...
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1answer
23 views

Complexity of “half cycle”

I'm working on the following problem: HALFCYCLE (HALFC): Input: A directed graph $G = (V,E)$. Output: Whether the longest cycle in $G$ has length $ \lfloor |V|/2 \rfloor$. Prove that if $\...
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1answer
29 views

Prove Subset-Sum is NP-complete - Alternative reduction?

It is well known the Subset-Sum problem is NP-complete. This can be shown using a reduction from the 3SAT problem. I am wondering: is there any other NP-Complete problem that could be reduced to the ...
3
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2answers
48 views

Proving a problem as NP-complete

According to this article, A problem X can be proved to be NP-complete if an already existing NP-complete problem (say Y) can be polynomial-time reduced to current problem X. The problem also needs ...
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1answer
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pseudo-polynomial reduction from 3-Partition to Partition

A problem $\Pi'$ is pseudo-polynomially reducible to the problem $\Pi$ ($\Pi' \leq_{pp} \Pi$) if, for any instance $I'$ of $\Pi'$, an instance $I$ of $Π$ can be constructed in pseudo-polynomially ...
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1answer
115 views

Proving NP completeness of maximal length path

I have this question to answer: For each node i in an undirected network $G = (N,E)$, let $N(i) = \{j \in N : \{i, j\} \in E\}$ denote the set of neighbors of node $i$ and let $c_e\geq0$ denote the ...
0
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1answer
38 views

Time complexity of subset sum problem with reals instead?

It is well known that the conventional subset sum problem with integers is NP-complete. What if the array elements can be any real numbers and also target sum can be any real number? Is it NP-complete ...
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1answer
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Prove/Disprove: Every two non-trivial NP-complete problems are decreasing reducible?

We say that two languages $L_1,L_2$ are decreasing reducible if there exists a polynomial time reduction $f:\Sigma^*\to\Sigma^* $ and there exists $n\in\mathbb{N}$ such that for every $x\in\Sigma^*$ ...
3
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2answers
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Why isn't the Generalized Super Mario Bros. obviously in NP?

It is shown in the paper: "Classic Nintendo Games are (Computationally) Hard" by Greg Aloupis, Erik D. Demaine, Alan Guo, and Giovanni Viglietta that the Generalized Super Mario Bros. (SMB, for short) ...
2
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1answer
27 views

Weak NP-completeness

I know that the Knapsack problem is weakly NP-complete. I also notice that on Wikipedia: "A problem is said to be strongly NP-hard if a strongly NP-complete problem has a polynomial reduction to it ...
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1answer
23 views

Reduction from NP-complete problem to unknown complexity problem and vice-versa

Suppose I have two problems: $B$, which is NP-complete, and $A$, of unknown complexity. Question: If I show that $B \le A$ I can state that $A$ is also NP-complete because the two required ...
2
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0answers
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NP-completeness of Induced disjoint paths between a set of sources and a set of sinks

In a given undirected graph $G(V,E)$, a set of $k$ paths is said to be induced if: They are vertex-disjoint. Each one is itself an induced path. No edge connects two vertices of two different paths. ...
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3answers
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How to solve the optimization of bin packing using the decision version

Let us say the optimization version of the bin packing problem asks you to give a packing using the fewest bins possible and the decision version asks if it is possible to pack the bins into $k$ bins. ...
3
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1answer
82 views

NP-completeness of Induced disjoint paths

In graph theory, it is well-known to be NP-complete the problem of given a set of $k$ pairs of source-sink, deciding whether there exists $k$ vertex-disjoint paths connecting these pairs. Our problem ...
0
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1answer
32 views

What are the current state of art approximation algorithm for NP-Hard problems? [closed]

I came cross some works try to use deep learning to approximate NP-Hard https://arxiv.org/pdf/1810.10659.pdf Though the paper seems to have very good results but based on the citations. I'm quit ...
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1answer
44 views

Parity Hamiltonian path problem

Wikipedia says that Hamiltonian path problem is NPC, but Parity Hamiltonian path problem (i.e., is there an odd amount of hamiltonian path) is P. Does a reduction from, e.g., SAT, to HPP, unavoidably ...
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1answer
30 views

Reduction from minimum dominating set to the set cover

To solve the min dominating set problem of a graph G, we can reduce it to a set cover problem. For example to find the MDS of the graph G: We can create an instance of the Set Cover problem by: ...
0
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1answer
68 views

Subset with modified condition, is it still NP-complete? [closed]

So I know the conditions required for a problem to be NP-Complete is that it has to lie within NP and has to be NP-hard. The given problem I have is subset sum. However, the conditions have been ...
0
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0answers
36 views

Is it NP-complete to test if a graph contains $t$ $k$-cliques?

Let $(G,t,k)$ - a graph with $t$ cliques with $k$ vertices (there are $t$ cliques of size $k$ in graph $G$), for $t,k > 100$. How to prove that $(G,t,k)$ is NP-complete? It is obvious that it is ...
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0answers
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Matrix covering by squares

I wonder about the following decision problem : Instance: We consider a $n\times p$ matrix $M$ of zeros and ones, and two integers $N$ and $k$. Question: is it possible to cover all the ones of the ...
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1answer
33 views

Reducing CLIQUE to Super Connector problem

I am trying to show that our problem is NP-Complete by reducing the known problem CLIQUE to our problem. Regular CLIQUE problem: Input: An undirected graph $G$ and a positive integer $K$. ...
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2answers
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Reduce 4-SAT to 5-SAT

given is a reduction from 4-SAT to 5-SAT. How is it possible to describe such a function? I found some informations about reduction 3-SAT to 4-SAT here, but it can't help me so much.
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1answer
34 views

If a problem Q is NP complete, is another problem reducible to Q also NP complete?

Let's say $\mathcal{P}$ is a yes/no prolem with an existing reduction to the problem $\mathcal{Q}$ (with time complexity $\mathcal{O}(n^2)$). $\mathcal{Q}$ is NP complete. Does this mean that $\...
3
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1answer
32 views

Finding a language that is $NP^L$-complete

I'm trying to prove a theorem and as a lemma I would like to identify an $NP^L$-complete language. I was thinking something like a machine that can decide $SAT$ equipped with an oracle for $L$ can ...
7
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1answer
1k views

Is this possible when it comes to the relations of P, NP, NP-Hard and NP-Complete?

I saw an image that describes the relations of P, NP, NP-Hard and NP-Complete which look like this : https://en.wikipedia.org/wiki/NP-hardness#/media/File:P_np_np-complete_np-hard.svg I wonder if ...
5
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1answer
154 views

Prove that “Finishing the degree in three years” problem is NP-Complete

I was asked in an interview the following question: We'll define the "Finishing the degree in three years" problem in the following manner: Given a list of courses $C=\{c_1, c_2,\ldots, c_n\}$, ...
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1answer
164 views

NP hardness of unique Puzzle Generation

Introduction For those who did not read my prior question, I have created an algorithm that generates n^2 x n^2 Sudoku Grids. Out of those grids I remove elements to give only one solution. The ...
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1answer
82 views

P vs NP question from GeeksforGeeks

From here: https://www.geeksforgeeks.org/algorithms-np-complete-question-2/ Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to ...
2
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1answer
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Proving NP hardness in Puzzle with SAT reduction

Introduction I have created an algorithm that generates n^2 x n^2 Sudoku Grids. Out of those grids I remove elements to give only one solution. The algorithm follows an infinite language based on ...
0
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1answer
49 views

Valid method to prove NP completeness of a problem?

Suppose we are given that checking if there is a Hamiltonian path in a graph is NP Complete (HP problem). I want to prove that given a graph, node x, and node y, checking if there is a Hamiltonian ...
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1answer
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3-Coloring Graph problem

Can we prove that the 3 coloring graph problem (where no two adjacent nodes have same color) is NP instead of NP-complete? $$\mathrm{3COLOR} = \{\langle G \rangle \mid G \text{ is colorable with 3 ...
2
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1answer
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Is maximum-leaves spanning tree np-complete?

How can we show that a maximum-leaves spanning tree is NP-complete? what other np-complete problem we can use as our reduction base? (maximum-leaves spanning tree: does G have a spanning tree with at ...
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0answers
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What would be a good way to prove NP-Completeness of Min-satisfiablity problem

I am trying to prove the NP-Completeness of Min-satisfiability problem which can be defined as: Given a CNF formula (Set of clauses of 1 or more boolean variables) and a number x, there exists a ...
4
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1answer
57 views

Is this problem that's similar to integer linear programming also an NP-complete problem?

I've come across this problem while trying to work out a table-formatting algorithm. It's very similar to standard linear programming (though it uses $>$ instead of $<$; I'm not extremely ...
0
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1answer
99 views

Complement of NP-complete can be in NP

Here are a couple of questions I struggle with. (We use $A'$ to denote the complement of the problem $A$.) A problem $A$ is NP-complete if and only if $A'$ is in NP? A class problem $A$ is NP-...
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1answer
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Does the intersection of VC and CLIQUE belong to NPC?

Define: $$L=\{(G,k) : G\text{ has a vertex cover of size at most $k$, and a clique of size at least $k$}\}$$ I need to determine whether $L\in \mathrm{NPC}$ or $L\in \mathrm{P}$. I suspect that $L\...
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1answer
79 views

Sudoku Puzzles in O log n time although inefficient

Suppose, I got a hypothetical fixed list of all possible general Sudoku puzzles. I then create the pseudo-code to demonstrate the algorithm. The algorithm does a search to compare the indexes of ...
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0answers
155 views

How can I reduce Subset Sum to Almost Subset Sum?

Maybe this is quite simple, but I am having some trouble how to do this reduction. I want to reduce Subset Sum to Almost Subset Sum. Subset Sum: given a set of positive integers $A=\{a_1,a_2, \dots,...
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2answers
39 views

Assume we have an algorithm HC for HAMILTONIAN CIRCUIT. How is it possible to convert the HC algorithm to an algorithm HP for HAMILTONIAN PATH?

My understanding is that I have to use the algorithm for Hamiltonian Circuit to help solve the Hamiltonian Path problem. My understanding is that we have to perform a reduction from Hamiltonian Path-...
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1answer
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Can a NP problem be reduced to another NP problem?

I have three related questions which have been bothering me for a while now... Suppose I have a problem $A$, which is in NP. Suppose there is another problem $B$ in NP, can I ...
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2answers
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Is “Reachable Object” really an NP-complete problem?

I was reading this paper where the authors explain Theorem 1, which states "Reachable Object" (as defined in the paper) is NP-complete. However, they prove the reduction only in one direction, i.e. ...
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2answers
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Symmetry of NP completeness

To show that some problem X is NP-complete, we usually show that it is in NP and that an efficient algorithm for deciding X implies an efficient algorithm for deciding some known NP-complete problem ...
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0answers
24 views

How to prune branches in a branch-and-bound solution for Flow Shop Scheduling?

I am implementing a Branch-and-Bound algorithm to find the optimal solution for the Flowshop Scheduling Problem, but I am stuck on the optimization phase, here is a rundown of the problem and what I ...
0
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0answers
46 views

P Langauage to NP Reduction in Polynomial Time [duplicate]

Let L be a language in P. Prove it is polynomial time reducible to any language in NP, including any language in P, which contains at least one string but doesn’t contain all the strings. I tried ...
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0answers
25 views

Where f(n) = n! belongs to? P, co-P, NPComplete or NPHard? [duplicate]

Where f(n) = n! belongs to? P, co-P, NPComplete or NPHard?
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The NP completeness proof for a variation of the 3CNF-SAT problem

There is a variation of 3CNF-SAT which is called 10-3-CNF-SAT = {<$\Phi$>: $\Phi$ is a satisfiable CNF formula with $\textbf{at most}$ 3 literals per clause and every variable occurs in $\textbf{at ...