Questions tagged [np-complete]
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138
questions
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Bounded-Frequency Minimum Set Cover Problem
Consider the special case of the minimum set cover problem where each element of the universe occurs in at most 3 sets.
Can this problem be solved in polynomial time?
Is there a nontrivial upper ...
6
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1answer
263 views
Cook inspiration for NP completeness
An academic descendant of Cook just lectured on NP completeness. He said that the idea came from a well-known theorem in first-order logic that talks about completeness of satisfiability for ...
1
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0answers
121 views
For what parameters is minimum distance hard?
It has been shown by Vardy that minimum distance of a code is NP-hard (see Alexander Vardy, “The Intractability of Computing the Minimum Distance of a Code,” IEEE Trans. Inf. Thy., Vol. 43 pp. 1757--...
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1answer
158 views
Lexicographic Boolean satisfiability
Maximal Satisfying Assignment (Lexicographic Boolean satisfiability / LexMaxSAT), the problem of finding the lexicographically maximum x_1, . . . , x_n ∈ {0, 1}^n that satisfies Boolean formula φ, or ...
13
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0answers
259 views
Is this problem on unambiguous finite automata NP-complete?
An unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such
that each word has at most one accepting path. In this post, for $n\in \mathbb{N}$, what I call an $n$-UFA (resp....
5
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1answer
408 views
Unary language examples between L and NP
I am looking for some examples of unary languages lay between $L$ and $NP$, i.e., $ L \subseteq NL \subseteq P = AL \subseteq NP $.
What I found after some search(e.g., Complexity zoo for unary ...
9
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0answers
133 views
Is 4-Coloring restricted to graphs with crossing number 1 NP-complete?
Planar graphs are 4-colorable.
Determining if a planar graph is 3-colorable is NP-Complete.
A graph with a crossing number 1 (graph such that it can be drawn with $\le 1$ crossing) is 5-colorable.
...
1
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1answer
88 views
Choosing one number from each set so that the sum of squares of each distinct number counts is minimized
Problem is as follows:
We are given $K$ subsets of $\{1,2,...,n\}$. We need to pick one number from each of these subsets such that $\sum_{i=1}^n p_i^2$ is minimized where $p_i$ is the number of times ...
1
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2answers
72 views
Disjoint subsets problem complexity
Is the decision problem below NP-complete?
Given sets $S_1, ... , S_n$, as well as bounds $b_1, ... , b_n$, is it possible to pick pairwise disjoint subsets $U_1, ... , U_n$ such that $U_i \subset ...
-5
votes
1answer
27 views
Polynomial-time reducibility of Primality and 3-SAT
Is 3-SAT $\leq_{p}$ Primality? And/or is Primality $\leq_{p}$ 3-SAT? I think the answer is no and yes, respectively, but I'm not sure. Any help would be appreciated.
Thank you.
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0answers
39 views
Efficient algorithm for finding segregators in a directed acyclic graph
Given a directed acyclic graph $G=(V,E)$, we define a $(\alpha,\beta)$-segregator of $G$ to be a subset $S$ of $V$ of size $\alpha$ such that no vertex in $G\setminus S$ has more than $\beta$ ...
2
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1answer
110 views
NP-completeness: sum of "some" paths in a spanning tree
I suspect this problem is NP-complete but I couldn't prove it, if anyone can help I'll be very grateful:
Instance: undirected, unweighted, connected graph $G=(V,E)$, positive integer $K \in \mathbb{Z}...
2
votes
2answers
368 views
Is the maximum independent set in cubic planar graphs NP-complete?
In their famous book, Garey and Johnson, write a comment that the maximum independent set problem, in cubic planar graphs is NP-complete(page 194 of the book). They say this is by a transformation ...
8
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7answers
886 views
NP-complete decision problems on deterministic automata
Do you know any NP-complete decision problems on deterministic automata? Most NP-complete problems that come to my mind are either (see, or here) graph theoretical, or involve some string rewriting or ...
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0answers
46 views
Minimum rank graph cut
Consider the following problem:
Input: A graph $G=(V,E)$ and a matroid $M$ on $E$, given by an independence oracle.
Task: Find a cut $C\subseteq E$ in the graph, such that the rank of $C$ in the ...
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0answers
118 views
Complexity of multi-objective optimization problems
How can we define and prove the worst-case complexity of multi-objective optimization problems (MOOP)?
It is easy to see that, if one of the objectives is an NP-Hard optimization problem, then the ...
2
votes
1answer
61 views
Maximum subgraph problem with unknown complexity
Let $Q$ be a polynomial time decidable graph property. In a graph let us call a subgraph $S$ a $Q$-subgraph, if $S$ has the property $Q$. Consider the following optimization problem:
Maximum $Q$-...
5
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0answers
99 views
Reconstructing a colored grid with vertical and horizontal shifts
Consider the following simple problem (puzzle): given
a $N \times N$ $c$-colored grid $G$
a $N \times N$ $c$-colored target grid $G_T$
a number $m$ represented in unary
Can we transform $G$ into $...
6
votes
1answer
336 views
Complexity of finding the largest induced subgraph with all even degrees
What is the complexity of the following problem?
Instance: Simple, undirected graph $G$, and a positive integer $k$.
Question: Does $G$ have an induced subgraph on at least $k$ vertices, such that ...
10
votes
1answer
741 views
Relationship between two graph optimization problems
Let $Q$ be a polynomial time computable graph property of simple, undirected graphs. Consider the following two optimization problems on any input graph:
P1. Find a largest induced subgraph of the ...
-4
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1answer
117 views
Example of decidable NP-hard problem that is not NP-complete [closed]
I am looking for an example of a decision problem which fulfills the following conditions:
1. It is decidable
2. It is NP-hard
3. It is not NP-complete
All my search attempts yielded examples that ...
1
vote
1answer
931 views
What languages can be reduced to a NP-complete problem in polynomial time
NP-complete: Language is NP-complete, when it is in NP and every problem in NP is reducible to it in polynomial time. But what languages are reducible to a NP-complete problem (for example SAT) in ...
4
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0answers
73 views
Short $\exists$SO sentences over strings that define an NP-complete problem
[Q1] I'm wondering if there are some "official" SHORT existential second order sentences with ONE binary relation, over strings (over a small alphabet) that define an NP-complete set.
(Something ...
10
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2answers
301 views
"Relatives" of the shortest path problem
Consider a connected undirected graph with non-negative edge weights, and two distinguished vertices $s,t$. Below are some path problems that are all of the following form: find an $s-t$ path, such ...
5
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0answers
60 views
Hardness result or reference for optimal Gaussian elimination process
I'm wondering if the following problem is NP-Complete or has any hardness result.
References on related problem are also welcome.
Input: integers $n\geq1,k\geq0$ and an invertible matrix $M\in\mathbb ...
2
votes
0answers
67 views
Hardness result or reference for a set partition problem
I'm wondering if the following problem is (or has been proven to be) NP-Complete.
Input: integer $n\ge0$, set $S_1,S_2,\ldots,S_{2n}$, set $T_1,T_2,\ldots,T_n$.
Accept iff: there exists $\{a_i,...
5
votes
1answer
111 views
$NP$ completeness of Hamiltonicity of cubic polyhedral plane graphs with bounded face degree?
Let $\mathscr{C}_d$ be the class of cubic 3-connected simple plane graphs, with face degree bounded by $d$.
Is there any $d$ such that Hamiltonian cycle is $NP$ complete on $\mathscr{C}_d$? If so, ...
11
votes
1answer
198 views
Natural candidates for NP-E and E-NP
It has been known since the early 70's that ${\bf NP}$ and ${\bf E}=DTIME(2^{O(n)})$ are not equal (because ${\bf E}$ is not closed under polynomial-time many-one reductions, in contrast to ${\bf NP}$...
0
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2answers
233 views
NP-hard problems on the class of caterpillars
My question is whether there exist an NP-hard problem that has only a caterpillar as input.
By saying only caterpillar as input, I wanted to emphasize that no function (eg: weights on vertices or ...
3
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0answers
249 views
new subset sum approach results
I have been working on a new approach for a subset sum exact solver, and the current state provides an algorithm operating on $O{n/2 \choose n/4}$, demonstrating as well the hardest target value is ...
1
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1answer
213 views
Does BQP contain any NP-Complete problem?
From the Wikipedia documentation, "the suspected relationship of BQP to other problem spaces" diagram suggests no intersection between NP-complete problems and BQP.
Has this been demonstrated or not?
0
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1answer
164 views
Subset Sum Problem and hard looking instances that are not really hard
I have been working in a subset sum solver (some new approach) and while working on the time complexity analysis I found what I describe below. Maybe this could explain why some "hard looking" ...
2
votes
1answer
168 views
Is balanced Hamiltonian cycle NP complete on maximal plane graphs?
I know that the Hamiltonian cycle is NP complete on the class of maximal plane graphs.
If we instead ask about balanced Hamiltonian cycles (i.e. same number of faces on both sides) on maximal plane ...
0
votes
1answer
252 views
A dominate vector subset sum problem
Let $k$ be some constants (e.g. one can take $k=2$ for simplexity), for any $u,v\in \mathbb{R}$, we say $u$ dominate $v$ if $\forall 1\le i\le k,~ u[i]\ge v[i]$, write it as $u\succ v$.
Consider the ...
4
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1answer
163 views
Complexity of finding Exact Size Cut-Sets in Bipartite Graphs
I am interested in the problem of deciding if a cut-set of a given size $k$ (i.e. the number of edges crossing the partitions is $k$) exists in a given bipartite graph (both the graph and $k$ are part ...
9
votes
2answers
464 views
NP-Complete Static Square Puzzles
In order to empirically test some CSP algorithms, I would like to compile a list of NP-Complete static board games. By static, I mean that a solution of the puzzle is simply an assignment of values to ...
7
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0answers
57 views
Complexity of deciding whether subspaces of Z_2^n cover every point 3*x times
When studying the complexity of checking identities in certain finite algebras, I came across the following decision problem:
Input: A positive integer $n \in N$ and a set of affine subspaces $H_1,...
4
votes
1answer
122 views
NP completeness of Hamiltonian cycle for the family of *dual graphs* to plane, cubic, triply connected graphs?
It is well known that the Hamiltonian cycle problem is NP-complete on the family of planar, cubic and triply connected graphs: https://epubs.siam.org/doi/abs/10.1137/0205049
For a problem I'm ...
11
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0answers
371 views
Error in paper "Some NP-complete geometric problems"?
The paper in question:
M.R. Garey, R.L. Graham and D.S. Johnson. Some NP-complete geometric problems .
This paper proofs the NP-completeness of some well-known problems, such as the Steiner Tree ...
16
votes
1answer
1k views
Password hashing using NP complete problems
Commonly used password hashing algorithms work like this today: Salt the password and feed it into a KDF. For example, using PBKDF2-HMAC-SHA1, the password hashing process is ...
0
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1answer
129 views
Is Prime Bounded Quadratic Congruence NP-complete?
Bounded Quadratic Congruence:
Instance: Three positive integers $a$, $b$ and $c$.
Question: Is there a positive integer $x<c$ such that $x^{2} \equiv a \, (mod \ b)$?
Bounded Quadratic ...
-1
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1answer
57 views
NP-Complete graph problems where a special vertex is given as input?
I am currently working on a graph theory problem where the instance includes a graph and a special vertex in the graph. I am trying to prove the NP-completeness of the problem as well as explore ...
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0answers
478 views
Is satisfying $\sum_{i=1}^{n}{x_i^{y_i}}=r$ NP Complete?
Question
I would like to show that satisfying $\sum_{i=1}^{n}{x_i^{y_i}}=r$ is NP-Complete.
Consider $L= \{(\bar{y},r):\exists \bar{x} \text{ such that } \sum_{i=1}^{n}{x_i^{y_i}}=r\}$.
Where $\...
1
vote
1answer
161 views
Can MONOTONE WSAT be in solved in polynomial time?
In the weighted monotone satisfiability problem (MONOTONE WSAT), the input is an n-variable MONOTONE CNF Boolean formula (when there is no a clause with a negated variable) and an integer k, and the ...
8
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0answers
145 views
Practical interactive proof schemes for NP-hard problems
Model-checking (in the sense of reachability in a succinct graph) is PSPACE-complete. SAT is NP-complete. Both problems are considered intractable, yet there exist tools capable of solving them on ...
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0answers
134 views
Generalized path cover problem in DAG
Let $G=(V,E)$ be a directed acyclic graph. Two vertices is transitive if there is a directed path between them. A Path Cover for a Set of Transitive Pairs (PCSTP) is a set of directed paths such that ...
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0answers
157 views
Are there any NP-complete for continuous mathematics? [closed]
Looking at this wiki page, it seems most NP-complete problems are based on discrete structures, such as graphs. What are some problems that involve real or complex analysis instead of discrete ...
8
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2answers
1k views
Isn't it "trivial" to represent/reduce any classical physics problem into a Spin-Glass which is NP-Complete?
In the late 80's there were several highly cited efforts to use Spin-Glass models to formulate other computational problems such as: Protein Folding and Neural Networks.
Isn't it straight forward to ...
0
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1answer
72 views
Maximize graph with k cut edge operations
I have undirected graph with N nodes each with some weight. There are M edges and in exactly K operations I want to maximize the XOR sum of connected components of the graph. ((n1 XOR n2 XOR n3) + (c1 ...
5
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2answers
191 views
Minimising the root-set of a spanning hyperforest of a hypergraph
I am interested in the complexity of a problem involving spanning hyperforests (a union of hypertrees, which covers all of the vertices) of a $k$-hypergraph. I describe the relevant definitions for ...
