The algorithms tag has no wiki summary.

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### finding dominating cycles in $2K_2$-free graphs

A cycle $C$ in a connected graph $G$ is called dominating if its complement $V(G)-V(C)$ is an independent set. H.J. Veldman proved in 1983 (Disc. Math. v.43, 281-96) a general result that in ...

**3**

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**1**answer

145 views

### How to generate $n$ FP32 rationals s.t. no two distinct k-el. subsets have same sum?

First some
Background: I have lots and lots of integer matrices, whose rows are $k$-combinations (without repetitions and sorted) of numbers from the set $S:=\{1,...,n\}$ and needed to be compared ...

**11**

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**1**answer

178 views

### Fastest algorithm to compute the width of a poset

An colleague recently came to me with a problem concerning the scheduling of tasks in the presence of constraints (of the kind: task $x$ can't begin until task $y$ has been completed). It turned out ...

**5**

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**2**answers

207 views

### Compute adjugate matrix over commutative ring

Let $A$ be a $n\times n$ matrix over a commutative ring. I'm looking for a good method to compute its adjugate matrix.
My current approach is to use the Cayley-Hamilton theorem:
$$\text{adj}(A) = ...

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**0**answers

110 views

### NP hard problems on geometric graphs

I have posted this question before but i don't feel i expressed my confusion clearly enough. So i would like to try and explain again. This is a proof of the minimum vertex cover for unit disk graphs ...

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**0**answers

64 views

### Max flow with minimal requirements algo problem

While applying the algorithm to solve the max flow of the network with minimal requirements on edges, I have encountered a problem.
The algorithm states:
For graph G
create an edge from target to ...

**5**

votes

**1**answer

448 views

### How to test if the power of some algebraic number is the rational combination of two specific algebraic numbers?

Suppose we are given three algebraic numbers $\alpha,\beta,\gamma$ by presenting their minimal polynomial (degree less than $m$), the goal is to compute all positive integers $n$ such that $\alpha^n$ ...

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**1**answer

176 views

### Resolvent of a triangular matrix

Suppose $A$ is a triangular matrix. What is the most efficient known algorithm to compute the polynomial (in $x$) matrix $(xI-A)^{-1}$?
Of course, $(xI-A)^{-1}= N(x)/p_A(x)$, where $p_A$ is the ...

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votes

**1**answer

97 views

### how to reduce 3-colorable graph to this? [closed]

suppose we have a finite set X and a set S of subsets of X and we want to determine is there a subset S' of S such that all members of X belong to exactly one set in S' I think the best problem to ...

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120 views

### E- and A-algorithms for finite arithmetic prime progressions and other sets

(EDIT from scratch).
Let $\ \mathbf a := (a_1\ \ldots\ a_n)\ $ be an increasing non-constant arithmetic progression of odd positive numbers. The goal here is to resolve efficiently one of the two ...

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**1**answer

159 views

### Decomposing representations of finite groups of Lie type via computer

This is related to my previous question here.
Let me remind you what that question asked:
Let $\text{St}_n(\mathbb{F}_q)$ be the Steinberg module (over $\mathbb{C}$) for ...

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**1**answer

59 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?

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117 views

### Explicitly showing that a free group is LERF [closed]

Let $F$ be a free group on a finite set $X$, and let $M$ be a finitely generated subgroup.
Marshall Hall's theorem states that $M$ is closed in the profinite topology on $F$. That is, $M$ is the ...

**8**

votes

**1**answer

345 views

### Algorithm to produce random number with a gamma distribution

I'd like to produce pseudo-random numbers with different distributions for a Monte Carlo simulation.
I've got the poisson distribution working nicely with an algorithm from Knuth. I'm having trouble ...

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**0**answers

137 views

### Trilateration issues, when circles don't intersect

I'm working on Indoor localization where I've deployed multiple iBeacons in my environment. I'm taking distances from all the beacons through their RSSI values. They are not 100% accurate though. Now ...

**0**

votes

**1**answer

83 views

### Using upper bound information in graph search

I am using A* (A-Star) to search a graph. A* algorithm takes advantage of the information $h(x)$, which is a lower bound of the distance between a vertex $x$ and the destination vertex.
In other ...

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votes

**1**answer

131 views

### DL-problem on abelian variety

Let $A$ be an abelian variety over $\mathbb{F_q}$ with dimension $n$. Let $q$ be a constant.
Is there polynomial algorithm of finding discrete logarithm in $A$?
UPD: really I don't undestend: can we ...

**3**

votes

**2**answers

333 views

### Find all faces in a graph from list of edges

I have the information from a undirected graph stored in a 2D array. The array stores all of the edges between nodes, e.g. graph[3] might be equal to [1,8,30] and represents the fact that node 3 ...

**2**

votes

**1**answer

335 views

### Solving assignment problem using Hungarian method vs min cost max flow problem

The traditional solution for the assignment problem is the Hungarian method - it's complexity is O(V^4) or O(V^3) if using Edmonds method.
However, it can also be reduced to a min cost max flow ...

**5**

votes

**3**answers

141 views

### Minimize distance between centroids of subsets of points

In a n-dimensional space, I want to divide a set of m points into v (non-empty) subsets.
I want to minimize the sum of the pairwise Euclidean distances between the centroids of the resulting subsets.
...

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**1**answer

304 views

### Polygamous stable marriage/ assignment problem

I'm not sure under which 'algorithm' it falls under, but here is the problem:
I need to match each person to 5 people from the opposite gender (each guy gets 5 girls, each girl gets 5 guys). Not all ...

**3**

votes

**1**answer

135 views

### Existence of subgraphs when given its degree sequence

For a given simple graph $G$ with $n$ vertices $v_1,v_2,\dots v_n$, the corresponding degree sequence is $d_1,d_2,\cdots,d_n$. My qusetion is:
How to determine whether there exist subgraphs in $G$ ...

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**0**answers

194 views

### Navigation in a graph

The problem
Let $G=(V,E)$ be a graph. $k = O\left(\log(|V|)\right)$ distinct vertices are picked randomly from $V$. We call the set of chosen $k$ vertices $T$.
Assumptions about the graph: You may ...

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**0**answers

208 views

### What is God's number for the WrapSlide puzzle?

WrapSlide is a slide-puzzle (reminding of Rubik's Cube) consisting of a 6x6 grid of coloured tiles which are separated into four quadrants of 3x3 tiles. When it is unmixed all the tiles in a quadrant ...

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**2**answers

311 views

### Does a classification of simultaneous conjugacy classes in a product of symmetric groups exist?

Let the symmetric group $S_n$ on $n$ letters act on $S_n^d=S_n\times\cdots\times S_n$ by simultaneous conjugation, i.e. $\pi\in S_n$ acts on $(\sigma_1,\ldots,\sigma_d)\in S_n^d$ by ...

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57 views

### Is there an efficient algorithm for sampling from the negative hypergeometric distribution? [closed]

I'm writing a small statistics library currently. One of the algorithms I'm implementing has two variants: one that samples the hypergeometric distribution and one that samples the negative ...

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82 views

### Containing a “fuzzy” ellipsoid within an ordinary ellipsoid

Consider the ellipsoid described by the inequality $(x - x_c)^T P^{-1} (x - x_c) \leq 1$, where the vector $x_c \in \mathbb{R}^n$ denotes the center of the ellipsoid and the symmetric positive ...

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vote

**2**answers

145 views

### Combinatorial optimization problem involving infinite spin system

In material science research, I am developing an algorithm to solve an infinite combinatorial optimization problem which I believe is the most natural problem when the system size goes to infinity.
...

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**1**answer

103 views

### enumeration of connected blocks in finite size square

Given a square of size n by m, how many ways could we choose sites, such that all the sites are connected?
By "connected" we mean "connected" by adjacent sites. We will illustrate by example, say, we ...

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84 views

### Complexity of an algorithm to solve linear diophantine equations

A friend of mine ask me yesterday a problem, however, the interesting part for me it is not his problem, but what I will ask here.
I want to know the optimal complexity of an algorithm (I mean the ...

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**1**answer

204 views

### Modular polynomials for elliptic curves point counting

The Schoof-Elkies-Atkin (SEA) algorithm (for counting points on elliptic curves over a finite field) performs computations over polynomials modulo some modular polynomials. Originally the "classical" ...

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**1**answer

72 views

### Paper on unit disk graphs

I was wondering if anybody knows of a 'link' to the paper by Marathe 1995 et al on analysis of the greedy algorithm for finding a Max independent set in Unit Disk Graphs?

**3**

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**1**answer

131 views

### Coloring algorithm maximising color difference between neighbors

Consider a graph and a set of ordered colors ${\cal C} = \{1,2,\cdots,C\}$. I want to color each node $i$ with a color $c_i\in{\cal C}$ so as to maximize the minimum color difference between two ...

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**1**answer

166 views

### Constructing sums of squares identities

Recall that a sum of squares formula for $[r,s,n]$ over a field $F$ is an identity of the form
$$ ( x_{1}^{2} + \cdots + x_{r}^{2})( y_{1}^{2} + \cdots + y_{s}^{2})
= ( z_{1}^{2} + \cdots + ...

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**3**answers

501 views

### Square filling self avoiding walk

I want to create an algorithm that fills a square grid with a random Hamiltonian path starting at a particular point. See this example.
One approach is to try a free direction as a next step, and ...

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**4**answers

559 views

### Algorithm to find the “optimal” path in a given graph

Assume that $G=(V,E)$ is an undirected connected graph and that $H: V \to \mathbb R$ is a function that assign at each vertex $v \in V$ its height $H(v)$. Think of the pair $(G,H)$ as an energy ...

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**1**answer

119 views

### Solution to generalized Sylvester equation

I am interested in solving generalized Sylvester equations (for $X$) of the form:
$$ \sum_{j=1}^k A_j X B_j^T = F, $$
where $A_j,B_j,X,F\in\mathbb{C}^{n\times n}$ and $k$, $n$ are integers. I will ...

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180 views

### What's the current state of one-rule semi-Thue system termination problem?

What's the current state of one-rule semi-Thue system termination problem? Search produces a lot of references, but it's hard to find out if decidability of this problem has been proven or not.

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### Recognizing Simplicial (Quasi)Fibrations

Let's say we are given two finite simplicial complexes, which I will suggestively call $E$ and $B$. We'd like an algorithm for the following decision problem:
Does there exist a simplicial map ...

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**2**answers

199 views

### Is this problem on weighted bipartite graph solvable in polynomial time or it is NP-Complete

I encounter this problem recently and I want to know whether it is NP-Complete or solvable in polynomial time:
Given a undirected weighted bipartite graph $G = (V, E)$ where $V$ can be partitioned ...

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votes

**1**answer

238 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 ...

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### 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 ...

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votes

**2**answers

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### 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 ...

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### 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 ...

**3**

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**1**answer

172 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 ...

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145 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 ...

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### 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 ...

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315 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 ...

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### 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 ...

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**1**answer

171 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 ...