Questions tagged [np-complete]
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136
questions
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3-partition problem is NP-complete. How about “N-partition problem”?
It is well known that 3-partition problem is strongly NP-complete.
(https://en.wikipedia.org/wiki/3-partition_problem)
Then, My question is, how about "N-partition problem"? Is it NP-...
-2
votes
0answers
39 views
How hard is this special 3-partition problem?
The definition of the original 3-partition problem is that: given a set $A$ of elements $A=\{a_1,a_2,...,a_{3m}\}$ and a positive integer $B$, and a positive size $s(a_i)$ for each $a_i \in A$ where $...
13
votes
0answers
251 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
votes
1answer
392 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
votes
0answers
132 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
vote
1answer
87 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
vote
2answers
71 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
26 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.
1
vote
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
votes
1answer
108 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
334 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
votes
7answers
843 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 ...
1
vote
0answers
45 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 ...
0
votes
0answers
109 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
60 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
votes
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
314 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
730 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
votes
1answer
114 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
850 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
votes
0answers
71 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
votes
2answers
278 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
votes
0answers
58 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
196 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
votes
2answers
231 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
votes
0answers
248 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
vote
1answer
202 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
votes
1answer
160 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
247 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
votes
1answer
146 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
460 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
votes
0answers
56 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
119 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
votes
0answers
370 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
votes
1answer
126 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
votes
1answer
56 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 ...
12
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0answers
474 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
157 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
votes
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 ...
1
vote
0answers
129 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 ...
1
vote
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
votes
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
votes
1answer
65 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
votes
2answers
189 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 ...
4
votes
1answer
184 views
Verifying that a reduction is correct
Alice has a function $f: \{0,1\}^* \to \{0,1\}^*$ which can be computed in polynomial time. She claims that $x \in \mathrm{SAT} \iff f(x) \in \mathrm{CLIQUE}$. Alice sends the circuit computing $f$ on ...
3
votes
2answers
180 views
Reduction of graph chromatic number to hypergraph 2-colorability
I'm following this paper titled "Coverings and colorings of hypergraphs" by Lovasz 1973, which is referenced in Garey and Johnson's Computers and Intractability, for the Set Splitting Problem. In this ...
