# Tagged Questions

**5**

votes

**4**answers

322 views

### NP-hard problems in linear algebra and real analysis [closed]

I am curious about NP-hard problems in linear algebra and real analysis. An example in linear algebra would be the calculation of the permanent.
I would thus like to collect in this thread a list of ...

**1**

vote

**1**answer

78 views

### Is undirected short-simple-path-through-3-vertices decidable in polynomial time?

Consider the following language:
$L=\{\langle G=(V,E),s,v,t,l\rangle\;|\;s,v,t\in V, l\in \mathbb{N} \wedge $ There exists a simple path from $s$ to $t$, going through $v$ of length $\leq l\}$.
($G$ ...

**3**

votes

**1**answer

132 views

### Is the domination number NP for non-bipartite graphs?

Calculating the domination number is an NP-Hard problem. Does it remain NP-Hard if we restrict it to non-bipartite graphs?

**2**

votes

**0**answers

109 views

### Partitioning a cubic graph into two induced cycles of equal order

I am aware that deciding the existence of a partition of the vertices of a connected graph $G(V, E)$ into two induced cycles is $NP$-complete(Theorem 2). Induced cycle is a cycle without any chord ...

**20**

votes

**1**answer

762 views

### How hard is reconstructing a permutation from its differences sequence?

My interest in combinatorially motivated computational problems led me to search for simple problems that turn out to be computationally hard. In this pursuit, I came up with a problem which I hope is ...

**2**

votes

**0**answers

125 views

### Intermediate $\mathsf{NP}$-complete problems?

Partition problem is weakly NP-complete since it has polynomial (pseudo-polynomial) time algorithm if input integers are bounded by some polynomial. However, 3-Partition problem is strongly ...

**1**

vote

**0**answers

70 views

### Are set covering problems with nonlinear cost functions NP-Hard?

Are set covering problems (set cover problem wikipedia) with a nonlinear cost function also NP-hard? Is there a general result about this?
To be more specific the cost function I am interested in ...

**5**

votes

**0**answers

106 views

### Are there sampNP-intermediate problems?

This questions is approximately cross-posted from theoretical computer science stackexchange
Ladner's theorem establishes that if $\mathsf{P} \ne \mathsf{NP}$ then $\mathsf{NPI} := \mathsf{NP} ...

**12**

votes

**6**answers

1k views

### SAT and Arithmetic Geometry

This is an agglomeration of several questions, linked by a single observation: SAT is equivalent to determining the existence of roots for a system of polynomial equations over $\mathbb{F}_2$ (note ...

**6**

votes

**1**answer

594 views

### NP-hardness of a graph partition problem?

I'm interested in this problem: Given an undirected graph $G(E, V)$, Is there a partition of $G$ into graphs $G_1(E_1, V_1)$ and $G_2(E_2, V_2)$ such that $G_1$ and $G_2$ are isomorphic? Here $E$ is ...

**0**

votes

**0**answers

279 views

### Is this minimization problem NP-Complete ?

We are given an nx(n+k) matrix A, with entries in GF(2), of the form A=(In|B) where In is a nxn identity matrix where the matrix B has no "zero" rows or columns.
The problem is to partition the ...

**0**

votes

**1**answer

500 views

### Knapsack Problem Specifics [closed]

(i) Are there limits on how many numbers must be in the set? { 1, 2 } or { 1, 5, 7, 8 , 9}
(ii) Are there limitations on how diverse or similar the numbers in the set can be? Coprime? Pairwise? { 1, ...

**2**

votes

**2**answers

527 views

### Could this be a NP complete?

Given a undirected and unweighted graph G(V,E). M is a subset of vertices of V.
s is a vertex in V - M.
Find an optimal tree T of G defined as:
(1) M and s are in V(T)
(2) Distance (which is ...

**7**

votes

**2**answers

974 views

### How to find nearest lattice point to given point in R^n ? Is it NP ?

Consider some lattice in R^n.
Take some point "P" in R^n (which does not belong to this lattice in general).
What are the algorithms to find some nearest lattice point to "P" ?
"Nearest" - means in ...

**5**

votes

**1**answer

810 views

### Is pattern recognition NP-complete?

Hello,
is the problem of pattern recognition (for a given sequence of n numbers, find the shortest Turing machine with an alphabet of 42 elements that will output these n numbers in, say, 5*n^3 time) ...

**0**

votes

**1**answer

503 views

### A few questions about Computational Problems Complexity Classification

(This might look like just a post to you and you might think I shouldn't have submitted it as a question here but in reality it is some questions put together, so I hope you don't close it)
I only ...

**2**

votes

**0**answers

230 views

### Complexity of a variant of the Mandelbrot set decision problem?

This is a modified version of a question posted on StackExchange TCS.
Mandelbrot set is defined using the complex equation $P_c (z)=z^2 +c$ where $c$ is a complex number. Let us define
...

**1**

vote

**0**answers

209 views

### Self-improvement property of optimazation problems?

Maximum CLIQUE problem is very hard to approximate. It has a self-improvement property defined using graph product which is utilized to prove hardness of approximation results. One such example is ...

**1**

vote

**0**answers

166 views

### Constructing hard inputs for the complement of bounded halting

If there is always a hard input for the complement of bounded halting, can that input be constructed?
More precisely, suppose that
for any $M$ accepting
$$
\text{coBHP}=\{\langle ...

**9**

votes

**4**answers

2k views

### Why relativization can't solve NP !=P?

If this problem is really stupid, please close it. But I really wanna get some answer for it. And I learnt computational complexity by reading books only.
When I learnt to the topic of relativization ...

**1**

vote

**0**answers

1k views

### Quantum computation implications of (P vs NP) [duplicate]

Possible Duplicate:
What impact would P!=NP have on the characterization of BQP?
Before I begin, I had a similar post closed for mentioning the recently released (to be verified) proof that ...

**11**

votes

**2**answers

2k views

### What impact would P!=NP have on the characterization of BQP?

Many complexity theorists assume that $P\ne NP.$ If this is proved, how would it impact quantum computing and quantum algorithms? Would the proof immediately disallow quantum algorithms from ever ...

**23**

votes

**2**answers

1k views

### Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?

Question. Given a Turing-machine program $e$, which
is guaranteed to run in polynomial time, can we computably
find such a polynomial?
In other words, is there a
computable function $e\mapsto p_e$, ...

**8**

votes

**3**answers

1k views

### Non-existence of algorithm converting NP algorithm to P algorithm?

[Edit: in the light of Nate Eldredge's answer below I rephrase the question]
P=NP is equivalent to the existence of a map of the following form:
Input: a polynomial-time non-deterministic Turing ...

**2**

votes

**1**answer

308 views

### poly-time algorithm to choose elements of sets

Let $A_1,A_2,\ldots,A_k$ be finite sets. Furthermore, for each $i\in\{1,2,\ldots,k\}$, let $B_i$ be a set whose elements are subsets of $A_i$.
Is there any polynomial-time algorithm that decides ...

**5**

votes

**1**answer

487 views

### Minimal Backtracking Proof Tree

When trying to prove that a particular instance of a problem like graph coloring or SAT is unsatisfiable, generally one explores the search tree using an algorithm like DPLL and the proof of ...

**6**

votes

**3**answers

2k views

### Is this a well known NP-complete problem?

I came across this problem recently and I wanted to know whether it was a well known NP-complete problem. I checked the library but could not find anything that matched exactly.
Given a directed ...

**4**

votes

**1**answer

786 views

### BPP being equal to #P under Oracle

Luca Trevisan here gives a randomized polynomial-time approximation algorithm for #3-coloring given an NP oracle.
In a similar vein, I was wondering if there were any results on ...

**18**

votes

**3**answers

2k views

### Satisfiability of general Boolean formulas with at most two occurrences per variable

(If you know basics in theoretical computer science, you may skip immediately to the dark box below. I thought I would try to explain my question very carefully, to maximize the number of people that ...

**13**

votes

**5**answers

3k views

### What techniques exist to show that a problem is not NP-complete?

The standard way to show that a problem is NP-complete is to show that another problem known to be NP-complete reduces to it. That much is clear. Given a problem in NP, what's known about how to ...

**6**

votes

**2**answers

1k views

### Best-case Running-time to solve an NP-Complete problem

What is the fastest algorithm that exists to solve a particular NP-Complete problem? For example, a naive implementation of travelling salesman is $O(n!)$, but with dynamic programming it can be done ...

**13**

votes

**4**answers

1k views

### Super-linear time complexity lower bounds for any natural problem in NP?

Do we know any problem in NP which has a super-linear time complexity lower bound? Ideally, we would like to show that 3SAT has super-polynomial lower bounds, but I guess we're far away from that. I'd ...

**6**

votes

**4**answers

2k views

### Characterize P^NP

What can you say about the complexity class P^NP, i.e. decision problems solvable by a polytime TM with an oracle for SAT?
Obviously P^NP is in PH somewhere between NP union coNP, and Sigma2 ...

**0**

votes

**3**answers

419 views

### How can one characterize NP^SAT?

Can you help me understand the class of problems solvable by a nondetermimistic Turing machine with an oracle for SAT running in polynomial time?