# Tagged Questions

**1**

vote

**1**answer

35 views

### How to select a subset of points from a universal to minimize the distance from outside to inside?

Here is the detailed problem.
I have a set of N points in K-dimension space, called U, and I want select M points of them, called S. For each point p in U, we define the distance from p to S as
$$ ...

**3**

votes

**1**answer

104 views

### A problem related to routing in a graph

I have come across a new problem - I want to know whether this problem is similar to some existing problem or not.
The new problem is this. There is a tourist who has a having the following ...

**2**

votes

**0**answers

27 views

### largest size for a randomness extractor

I am not so expert in theoretical computer science, so sorry if the question is trivial, i just could not find it in literature.
Suppose we have a source $X$ with min-entropy $\ell$, the randomness ...

**3**

votes

**2**answers

193 views

### Place N points in a 3d cube in a way that maximizes the minimum of their pairwise distances

Place $N$ points in a 3d cube in a way that maximizes the minimum of their pairwise distances.
The problem can easily be solved for $N\lt5$, but how to proceed for larger $N$?

**8**

votes

**1**answer

498 views

### How to check whether a positive integer can be written as linear combination of given others, where all coefficients are positive?

Let $n$, $k$ and $m_1, \dots, m_k$ be positive integers. Which is the most efficient
algorithm to find out whether there are positive integers $a_1, \dots, a_k$ such that
$n = \sum_{i=1}^k a_i m_i$?
...

**20**

votes

**4**answers

1k views

### Securing privacy of “who communicates with whom” under Orwell-like conditions

Assume that there is a big and powerful country with an
information-greedy secret service which has backdoors to all internet nodes
throughout the world which permit him to observe all exchanged data ...

**1**

vote

**0**answers

74 views

### Testing functional equivalence

We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...

**7**

votes

**1**answer

231 views

### Main problems on lattice-basis reduction algorithms (such as LLL)?

What are the main open problems on lattice-basis reduction algorithms (such as LLL)? I am looking for problems satisfying the following two conditions:
(a) their solution would likely be of some ...

**4**

votes

**0**answers

157 views

### Rough structure of the double coset space/Graph bijections up to automorphisms

I am dealing with bijective maps $\pi:\Gamma_1\to \Gamma_2$ between two graphs with the same number of vertices $N=O(10)$.
The graphs have a significant automorphism group (these are disconnected ...

**11**

votes

**4**answers

433 views

### Mathematics of privacy?

I wonder to which extent the current public debate on privacy issues (not only by state sniffing, but e.g. by microtargetting ads too an issue) offers interesting questions in mathematics?
Can we ...

**8**

votes

**2**answers

205 views

### Ideal Membership without Certificate?

I have a homogeneous ideal $I=\langle f_1,\ldots,f_r\rangle$ of the polynomial ring $\mathbb C[X_1,\ldots,X_n]=:R$ where each of the $f_i$ is actually over $\mathbb Z$. My computations are usually ...

**2**

votes

**1**answer

166 views

### Reducing the error of Algorithms by assigning variables formulas instead of values

Let me first give the intuition for my question: Suppose that you want to use a ruler to mark $n$ points in a line on a page, with 1 cm distance between neighbor points. There are two ways:
1- Mark ...

**6**

votes

**1**answer

356 views

### Is equality of terms for “real” numbers with roots, logarithm, exponential, sin, cos, and other trigonometric operations decidable with a Turing-machine?

If yes, how? Also, I know you can't do it for arbitrary statements about real numbers, but that's not what I'm asking, and by "real" numbers, I mean the numbers constructible from 1, -, /, and the ...

**0**

votes

**1**answer

249 views

### Counterexamples for this algorithm for recognizing lexicographic product of graphs?

Found a possible reduction from recognizing lexicographic product of graphs to 2SAT
(since 2SAT is polynomial, the algorithm is polynomial).
Can't prove completeness of the algorithm and since it is ...

**5**

votes

**1**answer

626 views

### How much does a quantum oracle to find a needle in a haystack really cost?

Among the basic algorithms of quantum computations Lov Grover's result on quantum search stands out, both in regards to its intrinsic interest, and for its undisputable elegance.
Grover's algorithm ...

**2**

votes

**1**answer

454 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 ...

**2**

votes

**1**answer

466 views

### Composite finite-state machines

A finite state machine, FSM, is a box with C input/output channels, and S states, and a fixed map $f : S\times C \to S\times C\cup {0}$. If a state $(c_i,s_j)$ is mapped to the 0 element it means it ...

**7**

votes

**2**answers

859 views

### Distribution of the computable numbers on the real number line

If we order all the positive computable real numbers $r_1,r_2,r_3...$ by their Kolmogorov complexity in some language $L$, then make a histogram plot of the $r_i$ on the real line, and we scale it ...

**12**

votes

**1**answer

2k views

### Evidence for integer factorization is in $P$

Peter Sarnak believes that integer factorization is in $P$. It is a well-known open problem in TCS to identify the real complexity class of integer factorization. Take a look at this link for Peter ...

**5**

votes

**6**answers

3k views

### Fast evaluation of polynomials

Hello everybody !
I was reading a book on geometry which taught me that one could compute the volume of a simplex through the determinant of a matrix, and I thought (I'm becoming a worse computer ...

**2**

votes

**3**answers

2k views

### Worst known algorithm in terms of Big-O (more precisely Big-theta)?

Hello,
I have been trying to find the worst algorithm in terms of it's Big-O function. By worst I mean n! is worse than n^2, n^n is worse than n!, etc. Essentially the worst algorithm would be the ...

**0**

votes

**0**answers

81 views

### Does there exist an algorithm for computing reachability in dynamic directed forests with fast update?

I'm interested in an algorithm which is able to compute reachability between any two nodes in polylog update (add or remove a valid edge) and query. I know that such an algorithm does exist for all ...

**2**

votes

**1**answer

185 views

### Parsing of Stochastic Contex-Free Grammars (SCFGs)

I am interested in parsing of general SCFGs.
I am aware of the Earley parser for the general CFGs. The only general algorithm for parsing SCFGs that I am aware of is the Earley-Stolcke parser : ...

**9**

votes

**1**answer

2k views

### All-pairs shortest paths in trees?

This is a reference request, since I'm sure what follows isn't new, but I can't seem to find it.
Suppose that we have a finite tree $T$ with non-negative weights on the edges. Naively, computing the ...

**5**

votes

**1**answer

331 views

### Drawing graphs on circles

Please consider the following problem:
Given: a simple graph (without self-loops and without multiple edges) $G$ on $n$ vertices.
Task: place equidistantly the vertices of $G$ on a circle of unit ...

**27**

votes

**1**answer

3k views

### An edge partitioning problem on cubic graphs

Hello everyone,
I already asked this question on the TCS Stack Exchange, but it has not been resolved yet. Maybe readers of this forum will have other ideas or information, although I suspect that ...

**6**

votes

**1**answer

421 views

### post correspondence problem variant

Is there an algorithm which takes as input two lists of words $v_1,...,v_n$ and $w_1,...,w_n$ over an alphabet $X$ and decides if there is an infinite sequence $(k_i)$ where $1 \leq k_i \leq n$ for ...

**2**

votes

**4**answers

730 views

### Enumerative algorithm through inclusion-exclusion

Hello everybody !
I wondered, without really knowing where to search, whether there was a "smart" way to enumerate/iterate over all the elements of a set which can be counted by inclusion-exclusion. ...

**3**

votes

**1**answer

472 views

### Approximating an integral representation of the Number Partition Problem

One can write out an integral whose solution gives the number of solutions to the NP-Complete Number Partition Problem and I'm wondering if anyone has an suggestions or ideas on who to solve or ...

**2**

votes

**0**answers

256 views

### Integer relation detection for Subset Sum or NPP?

Is there a way to encode an instance of Subset Sum or the Number Partition Problem so that a (small) solution to an integer relation yields an answer? If not definitely, then in some probabilistic ...

**1**

vote

**2**answers

801 views

### Practical use of probability amplification for randomized algorithms

Normally a 2-sided error randomized algorithm will have some constant error $\varepsilon < 1/2$. We know that we can replace the error term for any inverse polynomial. And the inverse polynomial ...

**2**

votes

**2**answers

331 views

### Efficient computation of AB^-1 for matrices

Hi there,
Sorry if this has already been asked before. I tried googling for it, but perhaps I could not find the right words to search for. My question is: Which is the fastest way to compute ...

**1**

vote

**1**answer

414 views

### Number of subset sums

Let $\mathbb{F}_q$ be a finite field with characteristic $p$ and $p < q$ (i.e. not a prime field). Let $D\subseteq \mathbb{F}_q$ be a some set with $|D|=n$. Find a non-empty subset ...

**3**

votes

**4**answers

1k views

### Does an “efficient” random number generator exist?

Given some number $n$ and a seed number $s$<$n$, I want a random number generator (RNG) that will go through all integers `<$n$ before coming back to $s$. The resulting random number must be ...

**4**

votes

**7**answers

1k views

### How to generate a net on a 8-dimensional sphere

Using Matlab, how to generate a net of 3^10 points that are evenly located (or distributed) on the 8-dimensional unit sphere?
Thanks for any helpful answers!

**0**

votes

**1**answer

171 views

### Building optimal rewriting rules.

Please give me some pointers where I can learn more about the following problem:
I have two alphabets A and B. A have a dictionary which contains words in A together with their translation in B (ie. ...

**1**

vote

**4**answers

1k views

### Finding the union of N random circles arbitrarily (or conspiratorially) placed on a two-dimensional surface

Please consider a two-dimensional surface populated with a set of Cartesian coordinates $(x_i, y_i)$ for $N$ circles with individual radii $r_i$, where $r_{min} < r_i < r_{max}$.
Here, the ...

**1**

vote

**2**answers

766 views

### Calculating the surface area distribution of two-dimensional projections for a polytope

My question concerns the existence of a nice (deterministic?) method/algorithm for calculating the distribution of surface areas for two-dimensional projections of an arbitrary polytope (or convex ...

**9**

votes

**2**answers

449 views

### When can a freely moving sphere escape from a 'cage' defined by a set of impassible coordinates?

To ask this question in a (hopefully) more direct way:
Please imagine that I take a freely moving ball in 3-space and create a 'cage' around it by defining a set of impassible coordinates, $S_c$ ...

**30**

votes

**7**answers

2k views

### What is the time complexity of computing sin(x) to t bits of precision?

Short version of the question: Presumably, it's poly$(t)$. But what polynomial, and could you provide a reference?
Long version of the question:
I'm sort of surprised to be asking this, because ...

**5**

votes

**1**answer

536 views

### Counting Eulerian Orientation in a 4-regular undirected graph

We would like to know how hard it is to count Eulerian orientation in an undirected 4-regular graph. For a given edge orientation to be Eulerian, we mean that every vertex has 2 in-edges and 2 ...

**1**

vote

**2**answers

645 views

### Find the subset of a line on a sphere “far” from a set of points on the sphere.

I have some code where the "hot part" relies on an inefficient solution to this problem.
Problem: I have 3 inputs:
a. A collection of N points on the surface of a sphere.
b. A line segment on the ...

**44**

votes

**4**answers

2k views

### What algorithm in algebraic geometry should I work on implementing?

This summer my wife and one of my friends (who are both programmers and undergraduate math majors, but have not learned any algebraic geometry) want to learn some algebraic geometry from me, and I ...

**0**

votes

**2**answers

758 views

### Travelling Salesman Problem [closed]

Does there exist an instance of the travelling salesman problem where the optimal solution has edges that cross?

**5**

votes

**1**answer

1k views

### Finding unknown integer-valued polynomials using inequalities

I've come across this interesting inequalities problem recently, which seemed straight-forward at first glance but has proven interesting enough to ask about it here.
Suppose you are given the ...

**1**

vote

**1**answer

2k views

### Closed form of a nonlinear recurrence sequence.

The master theorem seems to fail on nonlinear recursive functions. Is there a standard tool for finding the closed forms of recursive functions of this form?
The question comes from trying to find ...

**7**

votes

**2**answers

554 views

### Deciding membership in a convex hull

Problem: Given points $u,v_1,\dots,v_n\in\mathbb{R}^m$, decide if $u$ is contained in the convex hull of $v_1,\dots,v_n.$
This can be done efficiently by linear programming (time polynomial in ...

**14**

votes

**3**answers

1k views

### does the “convolution theorem” apply to weaker algebraic structures?

The Convolution Theorem is often exploited to compute the convolution of two sequences efficiently: take the (discrete) Fourier transform of each sequence, multiply them, and then perform the inverse ...

**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 ...

**11**

votes

**2**answers

2k views

### How to compute the rank of a matrix?

Okay, that's a misleading title. This is a somewhat subtler problem than undergraduate linear algebra, although I suspect there's still an easy answer. But I couldn't resist :D.
Here's the actual ...