**0**

votes

**0**answers

67 views

### Approximation for accumulative set cover

Let $S_1,\ldots,S_m\subseteq U$ be subsets of a set $U$ of size $\lvert U\rvert=n$. Over all permutations $\pi$ of the set $\{1,\ldots,m\}$, I want to maximize the quantity
\begin{equation}
\sum_{k=1}...

**1**

vote

**0**answers

181 views

### Optimize a convex hull on a 2D histogram so the selected points match a target shape

I have an image (can be 2D or 3D), and compute a 2D histogram of the image (for example, the pixel intensity and gradient along certain direction). There is a known target region $R^*$ in the image. I ...

**2**

votes

**1**answer

1k views

### Removing cycles from an undirected connected bipartite graph in a special manner

Consider an undirected connected bipartite graph (with cycles) $G = (V_1,V_2,E)$, where $V_1,V_2$ are the two node sets and $E$ is the set of edges connecting nodes in $V_1$ to those in $V_2$. We ...

**1**

vote

**2**answers

134 views

### Near-linear Function aproximation

Hi,
I have a growing, near-linear function, that has some "noise" in its linearity. Is there any solution, how to approximate this function ? I tried Neural Network, but ist not best...
Function ...

**0**

votes

**2**answers

382 views

### Enlcosing a set of ellipses within one ellipse

Hello,
Is there an algorithm that takes in a set of ellipses and gives back and ellipse that encloses the set?

**4**

votes

**4**answers

1k views

### When we use Bernstein polynomials in application

When it is preferable to use Bernstein polynomials to approximate a continuous function instead of using the only following preliminary Numerical Analysis methods: "Lagrange Polynomials", "Simple ...

**2**

votes

**0**answers

136 views

### A.G. Vitushkin's “Easily representable families of functions” - can it be generalized?

Background
In his monograph "Estimation of the complexity of the tabulation problem" (translated into English as "Theory of the Transmission and Processing of Information") Vitushkin studies ...

**4**

votes

**2**answers

559 views

### Set Cover:Greedy vs LP

Hi
Both, the greedy and the LP approach for Set Cover give a O(log n) approximation. Is there some inherent difference on the two approximation approaches?
thanks

**1**

vote

**1**answer

247 views

### Approximate Set Cover Problem by Rounding

Here is the simple algorithm for approximating set cover problem using rounding:
Algorithm 14.1 (Set cover via LP-rounding)
Find an optimal solution to the LP-relaxation.
Pick all sets $...

**0**

votes

**0**answers

161 views

### Pure greedy algorithm

I study pure greedy algorithms in different basises. I am interested in 1 one question: is there such a Riesz basis $D$ in Hilbert space and $f\in H$ such that
$\|f-G_m(f,D)\|>Cm^{-1/2}\lvert\{f}\...

**1**

vote

**0**answers

70 views

### An MST-like problem with vertex selection

Consider a planar pointset in a rectangle, where every point has a color (an integer label).
We need to select one point of every color, so as to minimize the cost of a planar MST of selected points (...

**3**

votes

**0**answers

238 views

### Place n telescopes on a sphere in R^d to see the whole sky

Where would one put $n$ telescopes on the surface of the earth
to see the whole sky as well as possible ?
Use the cosine metric to define how well we can see in direction $x$:
$ \qquad \text{cansee}( ...

**1**

vote

**0**answers

234 views

### Multiobjective semidefinite programming

Let $C$ be size $n \times n^{2}$.
Let $B$ be size $2^{g(n)} \times n^{2}$ where $g(n) > n$.
There is only one $\mathcal{1}$ per row of $C$ and remaining entries of $C$ are $\mathcal{0}$.
$B$ is ...

**1**

vote

**0**answers

470 views

### Representing vertices of a cube using linear combination of tensor product of smaller cubes

Let $n,N \in \mathbb{N}$ with $N \ge n^{2}$.
Let $F[i] = \square[i]$ refer to the cube which has vertices from $\{-1,0,1\}^{n^{i}}$ ($n^{i}$ tuple of alphabets from $\{-1,0,1\} = \square[0] = F[0]$)
...

**5**

votes

**2**answers

580 views

### Getting started: combinatorial optimization for computer scientists

I have a background in computer science and I am starting to work on some problems those are basically combinatorial optimization problems.
I have good knowleges of graphs, *-flow algorithms and so ...

**0**

votes

**0**answers

114 views

### sparsest cut always has solution

Hi!
How to prove that sparsest cut always has an optimal solution which is the cut for some vertex-subset.
Looks like it's should be a kind of fundamental theorem for sparsest cut. But I didn't ...

**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 ...

**4**

votes

**3**answers

387 views

### Approximating derivatives between gridpoints

Hi,
Suppose we have a grid (possibly irregular) of N function/value pairs, $(x_i, f_i)$, $i=1...N$. The function is differentiable everywhere at least twice (perhaps more).
What would be a good way ...

**0**

votes

**0**answers

351 views

### Approximate a piecewise linear path by a path with bounded curvature

I have a piecewise linear path in two dimensions (with finitely many pieces). I would like to approximate it by a curve whose radius of curvature is bounded away from 0 (i.e. I specify the bound a ...

**1**

vote

**2**answers

2k views

### Greedy approach to 0-1 Knapsack problem in specific instances

The 0-1 knapsack problem is known to be NP-complete, and the greedy approach by Dantzig (based on choosing on the basis of density or value/weight) can be shown to be suboptimal using counterexamples. ...

**1**

vote

**2**answers

671 views

### Approximate Algorithms for Poisson's Equation (PDE)

Are there some approximate or randomised algorithms to numerically solve Poisson's Equation in Partial Differential Equations.(http://en.wikipedia.org/wiki/Poisson%27s_equation). The best algorithms I ...

**3**

votes

**0**answers

204 views

### Algorithm for testing satisfiable fraction of linear equations mod 2

Hello
Let $F_{n,p}$ be a random process which generates a system of linear equations over $F_2$. The variables are $\{x_1, ..., x_n\}$ and for each of the $ \binom{n}{2}$ $i,j$ pairs, the equation $...

**2**

votes

**2**answers

366 views

### Approximation of conformal mapping as a sum of elementary conformal mappings

Hi,
I would like to approximate any 2d conformal mapping, as a sum of elementary conformal mappings. So I would have some basis, a conformal mapping with some parameters, and by adding several ones ...

**6**

votes

**3**answers

873 views

### Approximating e with 2s and 3s

How can I generate a series of 2s and 3s such that the average of the generated values (so far) is as close to e as possible?
For example:
...

**0**

votes

**1**answer

8k views

### HOW TO Generate Equation of a Curve Given (x,y) pairs - algorithm? [closed]

Hi,
How can I generate the equation of a curve that matches all arbitrarily given (x,y) pairs? I would like a polynomial of nth degree, where n does not matter, as long as the curve passes thru all ...

**4**

votes

**1**answer

757 views

### Hypergraph Chromatic Number vs Degree, Clique-Size

For a hypergraph let $\chi$ be the least number of colours needed to colour the vertices, so that in each edge, each colour is used at most once (i.e., the strong chromatic number). Let $\Delta$ be ...

**1**

vote

**2**answers

2k views

### Analyzing Weighted Set-Cover variant

A standard greedy algorithm for solving the weighted set-cover problem can be proven to be a $\log(n)$ approximation. I have a variant of weighted set cover, and I came up with a greedy algorithm for ...