All Questions
1,809 questions
0
votes
1
answer
145
views
A result about LSpace and RLSpace
I heard that there is a result which is proved that RL\subseteq L^{4/3}, but I don't which paper have proved it.
Can someone tell me this paper?
- 57
0
votes
1
answer
320
views
Correct way to conduct equilibrium scaling of linear/integer/MIP program
I would like to scale my linear/integer program and also mixed-integer program using the equilibrium scaling method. I have worked on two research papers and one research book. However, they did the ...
- 21
0
votes
1
answer
3k
views
Turing and Many one reductions in computability versus complexity
What are some non-trivial (please exclude poly time definitional difference) differences between Turing versus Many-one reductions in computability theory and those that occur in complexity theory?
- 13.9k
0
votes
1
answer
88
views
Intersection graphs
Does anybody know of a paper which proves that finding the maximum independent set in geometric intersection graphs is NP hard? Even general intersection graphs?
- 903
0
votes
1
answer
561
views
FO complexity class
I'm currently in a theory of computing class and as such I have been looking up information about P vs NP and other complexity classes out of curiosity. In the process I cam across a blog post ...
- 133
0
votes
1
answer
229
views
weaker oracle machine ?
My question is the following:
Can a (probabilistic, deterministic, ndtm) oracle turing machine $A$ calling an oracle residing in a superior (more difficult) complexity class $B$, have less power then ...
- 103
0
votes
1
answer
755
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 ...
- 103
0
votes
1
answer
539
views
Method for (binary) optimization under constraints
I would like to know if there is a method to solve the Problem.
Problem:
Maximize the following function: $$f(p_{1,i},p_{2,i},\dotsc,p_{m,i})=\sum_{i=1}^{n}\begin{bmatrix}p_{1,i} & p_{2,i} & \...
- 3
0
votes
1
answer
104
views
Turing degrees inside the $\Pi_1^0$ class with top Medvedev degree
I'm sure i have read that the following (or something that implies this) is true
Let $X$ be a $\Pi_1^0$ class with top Medvedev degree. Then for every
$x\in X$, there is $y\in X$ with $y<_T x$.
...
- 75
0
votes
1
answer
226
views
Fractional values in linear programming
Consider the linear programming problem
\begin{align}
f^* = \max_{x}&~p^Tx~\\~&A^Tx\leq b~,~0\leq x_i\leq 1
\end{align}where $p$ is a $n\times 1 $ vector, $A$ is a $n\times c$ matrix and $b$ ...
- 1,421
0
votes
1
answer
144
views
Maximize function on rotation matrices [closed]
Let $A$ be a fixed 3-by-3 matrix and $Q$ be a rotation matrix whose yaw, pitch, and roll angles are $\phi\in[0,\pi]$, $\theta\in[0,\pi]$, and $\psi\in[0,\pi/2]$, respectively:
\begin{equation}
Q=
\...
0
votes
1
answer
210
views
Is it theoretically possible to find a factoring algorithm that runs in polynomial time? [closed]
Given that we don't know if P=NP, what's to stop someone from finding tomorrow an algorithm that makes prime factoring, or any other trap-door function reversing for that matter, computationally ...
- 1
0
votes
1
answer
632
views
Baker, Gill, Solovay - Relativization [closed]
How am I supposed to read the P=?NP relativization proof? I am reading
Theodore Baker, John Gill, and Robert Solovay. Relativization of the P=?NP problem. Siam Journal of Computing, 4:432-442, 1975 [...
- 9
0
votes
2
answers
754
views
Relation between P and FP
For a decision problem that belongs to P can we assume that the equivalent function problem belongs to FP? For example: Is 8 a primal number? Belongs to P means that Find a primal number belongs to FP?...
0
votes
1
answer
36
views
Benefit of adding a trivial constraint to ILPs
let ILP be an integer linear program with constraints-matrix $\boldsymbol{\mathrm{M}}\in\mathbb{Z}^{m\times n}$ and cost vector $\boldsymbol{\mathrm{c}}\in\mathbb{Z}^n$,
${\boldsymbol{\mathrm{x}}^*}\...
- 13.2k
0
votes
1
answer
93
views
How quickly can this IQP or its MILP relaxation be solved
Let $A\in\{0,1\}^{(n,n)}$ be a $n$ by $n$ boolean matrix (in particular think of an adjacency matrix of a graph), and consider the following optimization problem:
$$\begin{align*}&&\max_{P\in\{...
- 71
0
votes
1
answer
314
views
NP-hardness of non-decision problems [closed]
how to show that non-decision problem is NP-hard?
So far I could find out that problems which are NP-hard do not have to be decision problems.
But how to show a non-decision problem is NP-hard?
Is it ...
- 51
0
votes
1
answer
131
views
How hard is a linear programming with a bounded constraint?
Background: I am reading Greg Kuperberg's answer to the question Deciding membership in a convex hull. I am thinking about the complexity of ''Deciding membership in a convex hull''.
Restate the ...
0
votes
1
answer
214
views
How do you call a linear programming problem when the solution should be "constrained" to a norm?
(apologies for the n00b question)
Let's say we have a vector of length $n$, with to-be-determined values: $a_1, a_2, ...,a_n$.
And we have information that partial sums of these elements are equal to ...
- 143
0
votes
1
answer
267
views
Algorithmically decide if an algorithm has optimal time complexity [closed]
Is there an algorithm with the following input and output?
INPUT: an algorithm computing a function $\mathbb{N}\to\mathbb{N}$. The algorithm is guaranteed to halt on all inputs.
OUTPUT: "YES"...
- 1
0
votes
1
answer
320
views
Sub optimal algorithm for linear programming
Consider the linear programming problem
\begin{align}
f^* = \max_{x}&~p^Tx~\\~&A^Tx\leq b~,~0\leq x_i\leq 1
\end{align}where $c$ is a $n\times 1 $ vector, $A$ is a $n\times c$ matrix and $b$ ...
- 1,421
0
votes
1
answer
118
views
Are all $P$-noncomputable sets $P$-random? [duplicate]
$P$ means polynomial complexity.
$S_p$ is class of all $P$_random sets, and $S_{pc}$ is class of all $P$ incomputable sets, is $S_{pc} \setminus S_p$ empty? If not empty, any example?
what is the ...
- 3,094
0
votes
1
answer
39
views
Gluing simplices through a common point/ realisation of a convex simplicial polytope
Given $m≥d+1$
a positive integer, is it always possible to find m d-dimensional simplices $\Delta_i=\mathrm{Conv}(M,V_{i,1},…,V_{i,d})$ such that
1) they all share the common vertex M
2) the ...
- 1,435
0
votes
1
answer
680
views
Solving a nonlinear equation system: is there a general result on complexity? [closed]
If there is a system of nonlinear equations and all variables are unbounded real numbers and the functions are continuous, is there a general result on the complexity of solving it? More specifically, ...
- 3
0
votes
1
answer
212
views
How to find out if a polytope contains a sphere?
Given a polytope described by linear inequalities $Ax \le b, x \in \mathbb R^n$, how do you find out if there exist a (non degenerate) sphere of dimension $n-1$ contained in the polytope?
Thanks!
- 225
0
votes
1
answer
130
views
Cascading minimization problems
Hi all. Suppose I have a linear programming problem on the vector variable $x$ that has many solutions and let $U$ be the set of these solutions. Suppose I have a second LP problem on $y \in U$. ...
- 57
0
votes
2
answers
891
views
Find both maximum and minimum values in linear programming problem
Hi all. I have a linear programming problem where I need to find both maximum and minimum values of the objective function. The optimal points are not relevant.
Is there an efficient way to do so?
- 57
0
votes
2
answers
257
views
Efficient computation of $E\left[\frac{1}{1+\sum_iX_i}\right]$ where $X_i$ is RV with Bernoulli distribution with different probabilities
Suppose we have the random variables $X_1, \ldots, X_n$ that have Bernoulli distributions with the (possibly different) probabilities $p_1, \ldots, p_n$. For example, $X_1$ = 1 with probability $p_1$ ...
- 21
0
votes
1
answer
427
views
Is the following statement a correct formulation of the (much doubted) P = NP conjecture?
"Call a Turing machine $A$ a d-machine if, for some polynomial $p(\cdot)$, when $A$ starts with any input string, say of length $n$, in its alphabet on its (otherwise blank) tape, it will halt in a ...
- 2,437
0
votes
2
answers
4k
views
Linear programming piecewise linear objective
I am fairly new at linear programming/optimization and am currently working on implementing a linear program that is stated like this:
max $\sum_{i=1}^{k}{p(\vec \alpha \cdot \vec c_i)}$
$s.t. $
$|\...
- 3
0
votes
1
answer
169
views
How to integrate an indicator function/constraint into the cost function of a linear program?
I have a mathematical model $P$ for which I optimize two cost functions say $F_1$ and $F_2$ subject to a set of constraints $C1$–$C10$.
In $F_2$, I want it to be included only when its expression ...
- 3
0
votes
1
answer
28
views
Calculating vertex potentials from optimal matchings
Question:
can the solution to the dual of a Linear Program be calculated directly from the solution of the primal Linear Program?
If yes, what are known algorithms and their bounds on complexity.
As ...
- 13.2k
0
votes
1
answer
125
views
Examples of real-time transcendental number and superlinear-time trancsendental number
Computation model is defined as Hartmanis and Stearns 4, it is well known that Liouvilles constant
$$C_L=\sum_{i=1}^{\infty} 10^{-i!}$$ is computable in real time or linear time 1, 5 especially ...
- 3,094
0
votes
1
answer
232
views
What are the odds for a random collection of numbers to have sum less than a certain number?
Let's say we have $I$ collections of numbers, $N_i$ numbers in each. A collection may contain repeating numbers. We randomly take one number from each collection. What is the probability for a sum of ...
- 131
0
votes
1
answer
110
views
Detecting non-negativity of a single constraint by polyhedral constraints - $I$
We consider $$\langle a,x\rangle=b$$ (linear constraints) where $x\in\mathbb R_{\geq0}^n$ and every entry in $a=(a_1,\dots,a_n)$ is in $\mathbb Z_{\geq0}^{n}$ (non-negative) and the entry $b$ is in $\...
- 13.9k
0
votes
1
answer
76
views
A question on graph partitioning
Given a connected un-directed simple graph $G=(V,E)$, is there a polynomial time algorithm to find the smallest subset $S$ of $V$ such that each node in $V \setminus S$ has at least 50% of its ...
- 1,216
0
votes
1
answer
354
views
Maximize sum of edge weights on spanning tree
Problem: Given a complete graph with n vertices, the edge weight between vertex $i$ and vertex $j$ is $b[i]\times b[j]$.
Under the condition that the degree of point $i$ on spanning tree is DEG $[i]$, ...
- 11
0
votes
1
answer
147
views
Complexity of edge coloring of class 1 graphs
We know that the decision problem of classifying the graphs as class $1$ or class $2$ (with respect to edge coloring) is NP-complete. But, suppose we have to prove a graph to be in class $1$. Does it ...
- 2,089
0
votes
1
answer
113
views
How do I solve this integer programming problem with non convex constraints?
I am not sure if this is the right place to post this question, please point me to the correct forum if I posted in a wrong place.
I have an optimization problem like this
...
- 103
0
votes
2
answers
556
views
Sparse dense matrix versus non-sparse dense matrix in eigenvalue computation
I have a matrix in the form of $2n\times 2n$ block matrix
$$
A = \begin{pmatrix}O& W\\
J& D\end{pmatrix}
$$
where, $O$ is an $n\times n$ zero-matrix; $W$ is a n-by-n diagonal matrix, $W = ...
- 91
0
votes
1
answer
140
views
Maximum partition of bipartite graph
Let $G = (U, V, E)$ be a bipartite graph. Let $w: E \to \mathbb{R}$ be a weight function on the edge set $E$. Given subsets $U_1,\ldots, U_k \subset U, U_i\cap U_j = \emptyset$ and a partition $V_1,\...
- 221
0
votes
2
answers
120
views
Reference request: dependence on linear constraints
Excuse me if my question is stupid. I'm seeking the references on the dependence of the (linear) optimization problem on (linear) constraints. Namely, consdier the following optimization problem:
$$P(...
- 1,835
0
votes
1
answer
2k
views
When to use non-negative-least square and least-square [closed]
What are the typical case we need to use Non-negative least squares NNLS
$$
||Ax - B||^2
$$
instead of least-square $$ Ax-B$$ (or vice versa)?
And is there any drawback in applying them on large $A$...
- 135
0
votes
1
answer
243
views
Does this algorithm terminate in all scenarios?
Let $x \in \mathbb{R}^p$ denote a $p$-dimensional data point (a vector). I have two sets $A = \{x_1, \dots, x_n\}$ and $B = \{x_{n+1}, \dots, x_{n+m}\}$, so $|A| = n$, and $|B| = m$. Given $k \in \...
- 123
0
votes
2
answers
244
views
Rewrite optimization objective
Hi,
I wanted to ask, under which conditions can one rewrite the optimization objective
$\min_x f(x)\;\;\;s.t.\;\;\;g(x) \leq s$
as
$\min_x g(x)\;\;\;s.t.\;\;\;f(x) \leq t$
I have particular ...
- 409
0
votes
2
answers
340
views
positive semidefiniteness: a psd matrix substracted by another rank 1 psd matrix
Given that $A$ is a positive semidefinite matrix, $x$ is a vector, $\lambda_0 \in [0, +\infty) $ is a real non-negative number. I want to know the answer to the following optimization problem.
$$
\...
- 101
0
votes
1
answer
2k
views
Find edge weights that fit given node weights
Let $G = (V,E)$ be a connected simple graph (unweighted, undirected, no selfloops) on $n$ nodes.
Let $\mathbf{d} := (d_1, d_2, ..., d_n) \in \mathbb{R}_{>0}^n$ be a vector of arbitrary given node ...
- 340
0
votes
1
answer
377
views
Algorithm for vector space
I have $n$ vectors $e_1 \in (\mathbb Z/2 \mathbb Z)^m,\dots,e_n \in (\mathbb Z/2 \mathbb Z)^m $
and a vector $ v \in (\mathbb Z/2 \mathbb Z)^m $
I need to find the better algorithm which answers ...
0
votes
1
answer
456
views
Is the Simplex Method still polynomial when all inequalities are through the origin?
Hello,
I want to solve a linear program using the simplex method, and I know that all my inequalities will pass through the origin (therefore, either my initial solution of (0, ... , 0) is optimal, ...
- 693
0
votes
2
answers
1k
views
Degenerate case of linear programming duality?
Let's say we have a maximization linear program that looks like this: maximize $\vec{c}\vec{x}$, subject to $\matrix{A}\vec{x} \leq 0$, $\vec{x} \geq 0$. If we take the dual, we have "minimize $0\vec{...
- 2,019