**3**

votes

**1**answer

100 views

### Covering a graph by trees with depth constraint

Given a graph $G$ and a depth constraint $h$, my question is: what is the complexity to find a tree cover of $G$, denoted as $T=\{T_1, T_2, ..., T_n\}$. For each $T_i$, its depth(height) is no larger ...

**2**

votes

**1**answer

65 views

### Minimum cover for sets in which each element appears in exactly 2 sets?

Is there an algorithm for finding minimal covers of a set of sets in which each element of the universe appears in exactly 2 sets? I realize that LP relaxation approximates this to within a factor of ...

**1**

vote

**0**answers

132 views

### How I can prove the equality $P^{P_{\operatorname{space}}}=NP^{P_{\operatorname{space}}}=P_{\operatorname{space}}^{P_{\operatorname{space}}}$ [closed]

I know how to prove that if $A \in P^{P_{\operatorname{space}}}$ then $A \in NP^{P_{\operatorname{space}}}$ and $A \in P_{\operatorname{space}}^{P_{\operatorname{space}}}$.
I don't know how to prove ...

**1**

vote

**1**answer

84 views

### How to complete the NP-hardness proof of GENERAL-SQUARE-PRODUCT?

I am interested in the complexity of the following problem:
GENERAL-SQUARE-PRODUCT
INSTANCE: Two sets $A=\{a_1,\ldots,a_n\}$ and $B=\{b_1,\ldots,b_n\}$ of integers, a positive integer $k<n$ and a ...

**2**

votes

**1**answer

116 views

### Minimal Support Solutions of a Linear System (Dissertation)

For a given $n \times m$ matrix A with $m>>n$ and a given vector $\vec b \in \mathbb{F}^{n \times 1}$, and given that $A\vec{x}=\vec{b}$ for at least one $\vec{x} \in \mathbb{F}^{m \times 1}$, ...

**1**

vote

**0**answers

19 views

### The complexity of Max-K interval selection

I came up with the following problem, but do not know how to analyze it.
Let $S$ be an ordered set of integers with size $n$ (i.e., $S=\{1,2,...,n\}$). An interval $INV(a,b)$ covers the elements in $...

**-1**

votes

**2**answers

99 views

### Is finding a local minimizer of a NP-hard optimization problem is still NP-hard [closed]

I was wondering if for a NP-hard optimization problem, I only want to find its local minimizer, is it still NP-hard or NP-hard is only true when trying to find a global minimizer?

**3**

votes

**1**answer

126 views

### Can we say that this problem is NP-hard?

I have an optimization problem of the form:
\begin{align}
&\text{maximize}\quad f(\mathbf{x}) = \dfrac{\sum\limits_{n=1}^{N}x_na_n}{1+\sum\limits_{n=1}^{N}x_nb_n}\\
& \text{subject to}\quad \...

**1**

vote

**1**answer

187 views

### On Knot Equivalence problem statement

How is the knot equivalence problem represented?
By this I mean I am looking for an analogy that compares with graph equivalence. For graph equivalence, we have two graphs $G_1$ and $G_2$ with ...

**2**

votes

**0**answers

126 views

### How hard is recognizing a permutation that is a square for the shift product?

This is a continuation of my attempts to generate simple combinatorial computational problems that turn out to be computationally hard (NP-complete). In this pursuit, I came up with a permutation ...

**0**

votes

**0**answers

69 views

### Efficient recognition of sequences sortable by transpositions?

While reading the post, Probability of generating a desired permutation by random swaps, by Aaronson, I got interested in this sorting problem:
Input: a sequence $A$ of $2N$ positive integers.
...

**2**

votes

**1**answer

157 views

### NP-hardness of finding maximum of minimum element in diagonal of a matrix

For $A = \{a_{ij}\} \in R^{n\times n}$, is finding
$$
\max_{\sigma \in S_n}\min_{1 \le i \le n} a_{i,\ \sigma_i}
$$
NP-hard?

**0**

votes

**0**answers

77 views

### Surd Partition Problem

Could the following "Surd Partition" problem be NP complete? Note that if the square roots are omitted in the following then the problem is well known to have a polynomial solution.
Surd Partition
...

**8**

votes

**2**answers

234 views

### Is this problem on weighted bipartite graph solvable in polynomial time or it is NP-Complete

I encounter this problem recently and I want to know whether it is NP-Complete or solvable in polynomial time:
Given a undirected weighted bipartite graph $G = (V, E)$ where $V$ can be partitioned ...

**3**

votes

**1**answer

140 views

### reduction to np hard ordering problem

I am trying to show a reduction from a problem of ordering problem to an np-hard problem that has approximation poly-time algorithm.
My problem is: I have M auctions and in each auction I have N ...

**3**

votes

**2**answers

664 views

### What impact would P=BQP have on NP?

Assuming P=BQP (ie we have polynomial time algorithms to solve all BQP problems) can we use it to prove that P=NP?
The argument is that since we have the Grover's algorithm which can solve NP ...

**7**

votes

**4**answers

892 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 ...

**2**

votes

**1**answer

184 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

154 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?

**1**

vote

**1**answer

452 views

### Simple example of why Differential Equations can be NP Hard [closed]

Just looking for a simple example of why Differential Equations can be NP hard
Edit:
It appears that the answer below may be what I was looking for, but I am clarifying just in case:
Slides 58-...

**9**

votes

**3**answers

435 views

### Conjecture on NP-completeness of tesselation of Wang Tile up to finite size

Motivated by these following questions on tessellation:
coloring in lattice
Reference for Wang Tile
Computational approach deciding whether a set of Wang Tile could tile the space up to some size
...

**0**

votes

**1**answer

872 views

### How to determine the distance between two matrices under the meaning of a matrix function? [closed]

Suppose a nonlinear infinitely continous differentiable function $f:\mathbb{D}\mapsto \mathbb{R^+}$, where $\mathbb{D}\subset\left\{X|\text{rank}{X}=2,X\in\mathbb{R}^{3\times 3}\right\}$ is a ...

**3**

votes

**0**answers

206 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 (...

**2**

votes

**3**answers

157 views

### Reference Request for: Finding Large Bipartite Subgraphs via Destruction of Odd Cycles in Graphs

From the observation, that a bipartite graph doesn't contain odd cycles, it would seem natural to attempt to destroy all odd cycles in the most efficient way, by either removing edges or vertices of ...

**30**

votes

**1**answer

1k 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

165 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 NP-...

**9**

votes

**0**answers

237 views

### Testing contrasts in statistics: Is this provably a hard problem, or not?

Scheffé's method for identifying statistically significant contrasts is widely known. A contrast among the means $\mu_i$, $i=1,\ldots,r$ of $r$ populations is a linear combination $\sum_{i=1}^r c_i \...

**1**

vote

**3**answers

232 views

### Strategic vertex labeling

We are given a graph $G=(V,E)$ with positive edge weights $w_{i}$ and numerical {0,1,-1} labels $l$ for all vertices . We know that $G$ has a subset $G'$ with all vertices labeled 0(all vertices with ...

**1**

vote

**0**answers

108 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 ...

**0**

votes

**2**answers

347 views

### Generating 3SAT circuit for Integer factorization example

I read somewhere that 3SAT can be used to solve Integer Factorization.
If that is true, could someone teach me a simple example of generating the 3SAT by using a small number? Let's say you are given ...

**1**

vote

**0**answers

135 views

### Non-trivial lower bound on the number of “Graph Diagonals”

The definition of Graph Diagonals, that are the subject of this question, is based on the notions of crossing edges and on connected graphs:
Two edges $AC$ and $BD$ of a complete, symmetric and ...

**5**

votes

**0**answers

119 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} \...

**13**

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 ...

**0**

votes

**1**answer

101 views

### A simplified/harder 2-sequence longest common sub-sequence (LCS) problem

Basically, its a 2-sequence longest common sub-sequence (LCS) problem.
What's so special?
1: each alphabet only occurs 2 times, one in each sequence, which means with no same alphabet in one ...

**7**

votes

**1**answer

242 views

### one-dimensional (sort of) tilings

Consider the following one-dimensional tiling problem. Each "tile" is a sequence of nonnegative integers. A "region" is also such a sequence. I can shift the "tiles", or reverse them. A tiling is ...

**2**

votes

**2**answers

317 views

### Need input on a potentially NP-hard maximal edge-weighted multi-cycle graph

I've posted a question on Stack Overflow regarding a seemingly NP-hard problem on maximization of weighted cycles in a graph problem.
One of the respondents cited Professor David Speyer's Math ...

**6**

votes

**0**answers

732 views

### Is Logical Min-Cut Problem, NP-Complete? [closed]

Logical Min Cut (LMC) Problem: Suppose that G = (V, E) is an unweighted digraph, s,t are two vertices of V, and t is reachable from s. LMC Problem states that how we can make t unreachable from s by ...

**2**

votes

**1**answer

602 views

### #P version of SUBSET SUM

The decision version of the SUBSET SUM problem asks the following: Given a set of integers $S =$ {$a_1, ..., a_n$}, is there a subset $S'$ of $S$ such that the sum of the elements in $S'$ is equal to ...

**3**

votes

**0**answers

1k views

### 0,1 solution to system of linear integer equations.

I have the following problem:
$A x = b$
where $A, b$ - $m \times n$-maxtrix and $m$-vector of nonnegative intgers (respectivelly).
$x \in \{0,1\}^n $ - vector of binary variables, which need to be ...

**6**

votes

**1**answer

877 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 ...

**5**

votes

**0**answers

273 views

### Any approximation algorithms for self-avoiding walks?

I've a graph whose edges are weighted by probabilities, perhaps all equal. I would like to compute the overall probability of traveling between vertices x and y in the graph after I delete each edge ...

**1**

vote

**0**answers

324 views

### Is this minimization problem NP-Complete ?

We are given an $n\times (n+k)$ matrix $A,$ with entries in $\mathrm{GF}(2),$ of the form $A=(I_n|B)$ where $I_n$ is a $n\times n$ identity matrix where the matrix $B$ has no "zero" rows or columns.
...

**1**

vote

**1**answer

807 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

544 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 ...

**2**

votes

**2**answers

184 views

### how to find vertex of parallelotope closest to given point P in R^n ? (Or minimize quadratic form over {+-1}) Is it NP ?

Consider a parallelotope in R^n and some point "P" in R^n.
What algorithms (except of brute force) can be suggested to find the closest vertex of paralleloptope to "P" ?
Is it NP ?
Parallelotope ...

**4**

votes

**1**answer

1k views

### Closest vector problem (=nearest lattice point) is trivial for “reduced lattice” ?

Consider some lattice in R^n. Take some point "P" in R^n (which does not belong to this lattice in general). The problem is to find "nearest" lattice point. The problem is known NP-hard in general it ...

**8**

votes

**2**answers

1k 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

981 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) ...

**4**

votes

**4**answers

632 views

### how to find vector $(\pm 1, \pm 1, \pm 1, … \pm 1)$ which is most close to given vector (r_1,…r_l) ? Is it NP-problem ? What algorithms are available ?

Given:
some vector $R=(r_1...r_l)$ - real numbers,
and a set of distinct vectors with $+1$ or $-1$ coordinates
$$\begin{array}{c} V_1=(c_{1,1} ... c_{1,l}),\\\
V_2=(c_{2,1} ... c_{2,l}),\\\
.....

**0**

votes

**1**answer

587 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 ...