The approximation-algorithms tag has no wiki summary.

**1**

vote

**1**answer

122 views

### Bivariate Function Approximation

I am working on a nonlinear control design and having difficulty in finding approximation of bivariate functions. Are there papers or methods discussing the following question:
For any bivariate ...

**0**

votes

**1**answer

149 views

### Efficient isomorphic subgraph matching with similarity scores

I'm a computer vision PhD student, and I'm looking for an efficient approximation to the following problem, which could end up helping in image to image matching. Failing that, pointers to relevant ...

**8**

votes

**0**answers

409 views

### How to evaluate binomial coefficients efficiently and as correctly as possible?

This question is more precisely about evaluation with a computer, of a binomial coefficient of the form $ \binom{x}{m}$ where $x$ is a real number and $m$ a rational integer.
The reason why I ask is ...

**7**

votes

**0**answers

106 views

### Nearest Point to a real algebraic set

Suppose I have a compact bounded real algebraic (eventually: or analytic or semialgebraic or semianalytic set) $V$ in $\mathbb R^3$ and a point $x\in\mathbb R^3$ not in $V$. How much do we know about ...

**5**

votes

**0**answers

232 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

**0**answers

133 views

### envelope function for a linear combination of gaussian distributions

Given a distribution $F$ defined as a linear combination of Gaussian distributions:
$F = \sum_{i=1}^n C_i*N(\mu_i,\sigma_i)$ with $\sum_{i=1}^n C_i = 1$
I want to find a Gaussian function $Q = ...

**3**

votes

**0**answers

226 views

### Tiling a rectangle with weighted cells (min-max problem)

I have been struggling with a research problem. The problem can be formalized as follows:
Given a $n\times m$ matrix $A$ containing cells with non-negative integer values, partition it in $J$ ...

**3**

votes

**0**answers

234 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}( ...

**3**

votes

**0**answers

194 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

**0**answers

60 views

### Convergence of Symmetric Iterative Proportional Fitting

Let $A$ denote a symmetric matrix of non-negative entries, whose rows (and columns) sum up to the all-positive vector $d := A\mathbf{1}$ with $\mathbf{1}$ the all-one-vector. Denote $D := diag(d)$ by ...

**2**

votes

**0**answers

39 views

### Norms of B-spline coefficients

In Shumaker's book (Spline Functions: Basic Theory), we know that the $l^\infty$-norm of B-spline coefficients is bounded above and below by the $L^\infty$-norm of the spline itself. Are there similar ...

**2**

votes

**0**answers

55 views

### Is the $d$-dimensional Arrangement of Trees still $NP$-hard?

The $d$-dimensional Arrangement Problem for general graphs is known to be $NP$-hard since the special case $d=1$ (OLA) already is (Garey et al, [1976]). For Trees however, the one dimensional case can ...

**2**

votes

**0**answers

119 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 ...

**1**

vote

**0**answers

134 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 ...

**1**

vote

**0**answers

67 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 ...

**1**

vote

**0**answers

223 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

452 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 $\{-1,0,1\} = \square[0] = F[0]$)
...

**0**

votes

**0**answers

29 views

### Inapproximability of logarithmic factor of independent set

The hardness result derived using PCP theorem for Independent set suggests that there exists some absolute constant $\epsilon_0$ such that for $0< \epsilon < \epsilon_0$, it is hard to ...

**0**

votes

**0**answers

51 views

### Any software that can symmetrize input sets?

Is there any software that contains symmetrization techniques ex. polarization, Steiner Symmetrization etc. I suppose not.
Which software would you suggest for rigid transformations?
Thank you

**0**

votes

**0**answers

16 views

### Estimating Missing Shortest-Path-Tree Distances from Point Coordinates

Problem:
given
a finite set of points $\mathcal{P}:=\lbrace p_i\in\mathbb{R}^2 \mid i\in \lbrace 0,...,n\rbrace\wedge i\neq j\Leftrightarrow p_i\neq p_j\rbrace$
a function ...

**0**

votes

**0**answers

31 views

### Approximation with Predefined Topology of Niveau Sets

Problem
given are
a finite, connected, undirected and, cycle-free graph (i.e. a "tree") $T(V,E)$, of which one of the vertices (w.l.o.g. $v_0$) is defined to be the root.
a planar imbedding ...

**0**

votes

**0**answers

58 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}
...

**0**

votes

**0**answers

154 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
...

**0**

votes

**0**answers

109 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 ...

**0**

votes

**0**answers

306 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 ...