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0
votes
1answer
131 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 ...
-4
votes
1answer
168 views

An algorithm and symbolic manipulation for IF-THEN-ELSE [closed]

CONCLUSION (so far)  Look at the parentheses theorem and at the comments below the question(s) :-) As for now, only Dan Peterson has truly addressed the issue. Q1   Does there exists an ...
2
votes
1answer
474 views

Efficient algorithms to determine the roots of: $p(x) = r^x $ in the finite field $GF(q)$, where $r$ a primitive root of the field

I need to make sure that no efficient (i.e., polynomial time) algorithm exists for the following problem: Exponentiating Polynomial Root Problem (EPRP) Let $p(x)$ be a polynomial with $\deg(p) \geq ...
10
votes
1answer
585 views

A generalization of the triangle counting problem for simple weighted graphs

One nice identity is $$tr(A^3)/6$$ which counts the number of triangles of a graph represented with adjacency matrix $A.$ It also implies that triangle counting can be performed in subcubic time. ...
0
votes
0answers
27 views

A Simple Uncomputable Function? [migrated]

Let F denote a computable function which takes an integer and returns an integer. Is "checking whether F has a finite null space" computable (using an algorithm which works for any F)? I believe ...
10
votes
1answer
358 views

Faster multiplication with a restricted set of multiplicands?

Let $A$ be a set of $k>1$ distinct elements from a semigroup. We wish to compute the product $$ p=b_1 b_2 \cdots b_n$$ where each $b_i\in A$. Clearly $n-1$ multiplications suffice to compute $p$; ...
0
votes
0answers
46 views

Calculating the longest Bracelet(s) Common to a Set of Bracelets

I would like to know, if the following problems has been studied before: let $\{B_1, ..., B_n\}$ be a set of Bracelets with the same set $\{\beta_1, ..., \beta_k\}$ of beads, what is the ...
4
votes
2answers
333 views

Are there any patterns in simple continued fraction expansions of algebraic real numbers?

As we know there are patterns in simple continued fraction expansion of quadratic algebraic numbers,are there any patterns in simple continued fraction expansions of other algebraic real ...
2
votes
0answers
160 views

Computing the chromatic polynomial of graph modulo $x-3$

The chromatic polynomial of graph $P(G,x)$ is univariate polynomial which counts the number of colorings of $G$ with $x$ colors for natural $x$. Graph is not $k$ colorable iff $P(G,k)=0$. The ...
12
votes
1answer
509 views

Stable matchings when switches have costs

The Gale-Shapley algorithm finds a stable matching in the complete bipartite graph, for any preference matrix. It's also well-known that stable matchings don't always exist in the complete graph ...
3
votes
1answer
160 views

An efficient method to find the MLE of the combination of two point processes

I have a point process defined in two parts as follows. Consider first the main process which we call $A$ which is homogeneous Poisson process with conditional intensity $$\lambda(t) = \mu$$ For ...
27
votes
3answers
2k views

Can assignment solve stable marriage?

This is an excellent question asked by one of my students. I imagine the answer is "no", but it doesn't strike me as easy. Recall the set up of the stable marriage problem. We have $n$ men and $n$ ...
2
votes
2answers
222 views

Finding the set of all $0-1$ vectors in an affine subspace

We are given a $0-1$ matrix $A$ with constant row and column sum, and we need to find out if there exists a $0-1$ vector in the solution space of $Ax = \mathbf{1}$ over $\mathbb{Q}$ (or $\mathbb{Z}$) ...
3
votes
0answers
127 views

Algorithm to compute a common denominator of a finite set of rational numbers

Let $x_1,\dots,x_n \in \mathbb{Q} \cap (0,1)$ be fixed, but unknown, and assume that we know a number $K \in \mathbb{N}$ such that there is a number $N \in \{1,\dots,K\}$ such that $x_1 N,\dots,x_n N ...
4
votes
4answers
304 views

Linear complementarity problem - Tridiagonal and Convex Case

I need an algorithm for the following LCP: $\mathbf{Mz}+\mathbf{q} \ge \mathbf{0}$ $\mathbf{z} \ge \mathbf{0}$ $\mathbf{z}^{\mathrm{T}}(\mathbf{Mz}+\mathbf{q}) = 0$ Here, $\mathbf{M}$, is a ...
3
votes
0answers
39 views

Algorithm to construct metric space endomorphism with controlled square

Given a finite metric space $(M,d)$ with parameters $K \geq 1$ and $\epsilon > 0$, I'd like to algorithmically check for the existence of a non-identity map $\phi:M \to M$ which happens to be ...
7
votes
0answers
91 views

Algorithms for computing the Resilience of Graphs

The definition of resilience with a graph $G$ w.r.t to a monotone property $\mathcal{P}$ is well known. (Global resilience) Let $\mathcal{P}$ be an increasing monotone property. The global ...
4
votes
2answers
334 views

How to tell if two or more knots are linked

Given a number of knots, I would like to know if they are linked. I know that the linking number can tell if two knots are linked. There is any method that completely solves this problem?
-4
votes
1answer
144 views

Bipartite graph [closed]

First of all, thank you for your time to reading my post. I am a researcher but not a mathematician, i have some difficulties in solving a math problem, that why i am here to ask your help. I just ...
2
votes
2answers
88 views

Sampling from maximally skewed stable distribution

I am reading a paper which refers to a maximally skewed stable distribution $F(x;1,-1,\pi/2,0)$ . Is there an efficient way to sample from this distribution? If $X$ has distribution ...
6
votes
1answer
216 views

Fast construction of straight line programs?

Given a group $G$ and a set of generators $A$, we can ask ourselves (and do ask ourselves all the time) to bound the diameter of $G$ with respect to $A$. The diameter, let us recall, is defined to be ...
26
votes
1answer
413 views

Decidability of equality of expressions built using 1,+,-,*,/,^

Consider expressions built using number $1$, arithmetical operators $+, -, *, /$ and exponentiation ^ (in case of multiple values, the principal value is assumed, the same way as it implemented in ...
5
votes
1answer
175 views

Estimate the rank of a vector

Consider {0,1}-vectors $v$ with $n$ elements. For each $i\in[n]$ we are given $p_i = P(v_i = 1)$ and let us assume the $v_i$ are independent. We can therefore associate a probability to each of the ...
9
votes
1answer
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 ...
1
vote
0answers
19 views

Minimal rectangular confidence regions

For a given multivariate pdf $f$ (mainly the gaussian one) I'm looking to compute a minimal rectangular confidence region for a given level $\alpha$. For example, I would like to solve problems of the ...
3
votes
2answers
126 views

All Integers from the Smallest Digit Stream with a Window Filter

Let's represent integers with D digits where each digit has B values (i.e., the base is B and we effectively work only with integers between 1 and B^D). Is it possible to choose a single ...
4
votes
0answers
91 views

A question on hyperplanes in partial linear spaces and hypergraphs

A partial linear space (or a linear hypergraph) is a point line geometry $(P,L,I)$ where for every pair of points there is at most one line incident with both of them. A hyperplane in a partial linear ...
1
vote
0answers
139 views

Is finding a single vector in the null space as difficult as discovering the whole null space?

Let $A \in \mathbb R^{k\times n}$ be a matrix of rank $k$, where $k \ll n$. One can use Gaussian eliminations to discover $\operatorname{null}(A)$ at the cost of $O(nk^2)$. My question is: Is the ...
6
votes
1answer
200 views

Shortcut from discrete Fourier transform F{x} to zero-padded F{x:0…0}

Summary: Given $X$ (the discrete Fourier transform of some unknown vector $x$ of length $N$), is there any shortcut to computing $X'$ (the Fourier transform of $x$ after padding it with $N$ zeros)? ...
7
votes
1answer
516 views

Can the Legendre symbol be calculated in polynomial time?

Is there an algorithm which on input "$(a,p)$" (where $0\leq a<p$ are integers) takes time polynomial in $\log p$ and outputs "NOT PRIME" if $p$ is not prime and otherwise outputs the Legendre ...
4
votes
4answers
383 views

Determine if a graph has a large clique

This question is quite specific and practical. I hope it is still relevant for MO and will not be removed. I have a collection $\mathcal{C}$ of graphs having from 5000-6000 vertices and edge density ...
1
vote
1answer
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 $$ ...
17
votes
0answers
151 views

A small unavoidable collection of subgraphs

What is the smallest number S(k,n) of unlabeled graphs on k vertices such that every simple graph on n vertices contains at least one of these as an induced subgraph? I'd like to avoid exhaustive ...
1
vote
0answers
26 views

Heuristic for choosing n-vectors from n-sets

my given problem is: choose n-vectors from n-sets (one vector from each set) so that the biggest element in the sum of the chosen vectors is minimal. Unfortunately the problem is NP-hard. So I'm ...
2
votes
1answer
114 views

Galois Connections: algorithmic generation

Given two finite posets $P,Q$, is it known any algorithm to count and/or generate every Galois Connection between $P$ and $Q$ ? I'm looking for references about this problem.
5
votes
1answer
137 views

coin reversal puzzle with one hand and two stacks

Suppose that you have N labeled coins pinched in one stack in your fingertips (your palm is above your fingers and your palm is facing down, so that you can drop as many coins as needed from the ...
10
votes
1answer
277 views

Explicit algorithm for composing permutations in factorial notation

Given two permutations p1 and p2 in factorial notation, is there an algorithm which computes their composition directly, i.e. without translating to a different notation (like Cauchy's 2-line ...
3
votes
2answers
172 views

Combinatorial design for minimization problem over binary strings

Suppose the cost of a binary string $B$ of length $k$ is the number of $1$s that occur before the last $0$. For example, $1110$ has cost 3 while $0111$ has cost 0. Now suppose you can choose $k$ ...
35
votes
1answer
1k views

improving known bounds for Pierce expansions; cash prize

Here's a problem that I thought of back in 1978 or so, and only a little progress has been made on it since then. I still think about it from time to time, but probably not that many people have ...
8
votes
3answers
514 views

Changing combination lock [closed]

Suppose you have a combination lock (n digits, m symbols) that is unlocked by one specific n-digit key sequence. However, trying a wrong key changes it according to an fixed but unknown function: new ...
16
votes
2answers
2k views

Inverting the totient function

For what values of $n$ does the equation $\phi(x) = n$ have at least one solution? Is there any efficient way to check it for a given $n$? It obviously has no solutions for odd $n$. And the smallest ...
1
vote
5answers
1k views

The Inverse of the Euler Totient Function

How can we calculate the cardinality of the inverse of Totient function of any positive integer n ? I tried going through this paper, but I couldn't understand the procedure. Thanks
3
votes
1answer
178 views

Generalization of notion of convexity

I am searching for the correct term for the following, if it exists. A set $X\subset \mathbb{R}^2$ is called $r$-convex if for any two points $x_1, x_2\in X$ such that there exists an arc of radius ...
27
votes
1answer
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 ...
1
vote
0answers
61 views

Lanczos algorithm with thick restart on a dynamic matrix

currently, I'm working on a way to compute the 2 biggest eigenvalues of a real, symmetric, huge and sparse matrix that changes a few entries from time to time. The problem should be solved using an ...
3
votes
1answer
105 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 ...
0
votes
0answers
57 views

Find minimal set of progressions which intersections, unions or negations covers given set

Given an integer $N$ and a set of integers in $[1; N]$. Find a minimal set of integer arithmetical progressions such as given set can be covered using operations $A \cap B$, $A \cup B$ and $\overline ...
1
vote
1answer
79 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 $\leq l\}$. ($G$ ...
7
votes
2answers
266 views

get a point in polygon (maximize the distance from borders)

I have several 2D polygons represented by lists of xy-coordinates of their vertices. It is needed to get several points inside the polygon so that they lie possibly far from the polygon's borders ...
2
votes
2answers
185 views

Integers up to n having an even number of trailing zeros in their factorial

It is well-known that the number of trailing zeros in the factorial $k!$ is given by the nice function $$ z(k) := \sum_{i \ge 1} \left\lfloor \frac{k}{5^i} \right\rfloor. $$ Now assume that we want ...