# Tagged Questions

Combinatorics (combinatorial analysis) is a branch of mathematics that studies the discrete objects, the set (a combination, permutation, deployment and transfer of elements) and the relationship to them (eg, partial order).

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### Algorithm to generate all vectors of integers with magnitude between $n\pm \delta$

I am working on an program to compute the structure factor of a given configuration of particles, and I need an efficient algorithm to generate all the possible vectors with integer coordinates and ...
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### Picking n integers from n different sets summing to a given value

Given a set of integers $\{l_1,l_2,\ldots,l_n\}$, where each integer is associated with a set $m_k\in\{-l_k,-l_k+1,\ldots,l_k\}$, I need to find all combinations $\{m_1,m_2,\ldots,m_n\}$ that sum to a ...
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### Striking examples of success of local search algorithms

In N queens problem https://en.wikipedia.org/wiki/Eight_queens_puzzle, trying to find solution by backtracking encounters difficulties quite fast (even for SWI-Prolog, http://swish.swi-prolog.org/...
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### Generating Combinations

I'm trying to find and print all the combinations of specific sizes that are less than or equal to a max size by building an algorithm in Google Sheets. For example, I have four sizes: 2.75, 4, 5, and ...
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### Optimal distribution of zeros and ones over matrix

I have the following problem: Given a matrix with n rows and m columns. Some elements of the matrix are unavailable. For each column, you have a set containing a number of zeros and ones which must ...
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### Clustering by shared subsequence

I have a question that relates to the classical "longest common subsequence" problem. I'll give the background to the problem, but you could skip to the formulation below if you like Let's think of ...
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### Pickup and delivery problem with time windows and container repositioning

Given a set of ships, harbors, batches, containers, and, a matrix of distances between harbors. At any given point in time a harbor has some number of containers which can either be available or used ...
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### Looking for a C/C++ implementation of the Hungarian method for real-valued cost matrix

I am looking for a C/C++ implementation of the Hungarian method for solving the linear assignment problem with real-valued cost matrix. Some implementation I found, such as this one, only work for ...
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### Sum of Inverse of Variables in an Optimization Problem

I have the following optimization problem: $$\begin{array}{ll} \text{Minimize} & \frac{1}{x_1} + \frac{1}{x_2} + \ldots + \frac{1}{d_n} \\ \text{Subject to} & A x \leq b \end{array}$$ where ...
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### Algorithm for generating the next m-tuple of integers, subject to constraints

I am looking for an algorithm with the following characteristics: It is used to generate the set of integer vectors $\mathbf k=(k_1,\ldots,k_m)$, where $k_i\leq K_i$, $k_i\geq 0$, and $K_i$ are ...
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### Optimal partitioning of a graph

Consider a planar graph, where each node is associated with a weight. I would like to partition the graph such that the sum of the node weights in each group satisfy a minimum requirement. However, I ...
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### Evolutionary algorithm - Traveling Salesman -fitness function

I'm trying to solve this problem using genetic algorithms and am having difficulty choosing the fitness function. My problem is a little different than the original Traveling Salesman Problem, since ...
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### What strategies one can use to keep maximum number of non attacking pieces on an $n \times n$ chess board? [closed]

What are the strategies one can use to keep maximum number of non attacking pieces (all pieces other than pawn) on an $n\times n$ board? It is like an $n$-queen problem but here instead of only queen ...
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### How can I compute whether a sequence is an even or odd permutation of an increasing sequence? [closed]

Variants of this question have been crossposted to Stack Overflow and Mathematics Stack Exchange. Additional answers may be found at these other sites. Computational Science People: I originally ...
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### Trying to implement a simple/efficient combinations function in MATLAB

So, recently, I have found myself in the position of having to implement a combinations function in MATLAB. What I mean by this is the following: I simply need to list all possible combinations for an ...
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### Parallel algorithm to use in place of PORTA?

We currently use PORTA software to find the list of facet-defining inequalities (FDI) for polytopes that we work with. For certain polytopes, PORTA works fine. But because it is a serial algorithm (...
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### Improve optimization over 'mapping' of indices

I have two tables at my disposal, one work dataset and one reference dataset. Each dataset has got two columns, lets say these are fields A and B. I would like to associate the rows in the reference ...
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### Generating lattice clusters/graphs in parallel

I'm trying to generate all graphs with n or fewer vertices that can be embedded in some lattice, eg square, triangular, Kagome. Do there exist algorithms to both enumerate and draw these graphs? What ...
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### Algorithm for generating all cartesian products, without rotations

(Not sure if that's the right SX site? I don't need actual code, so…) I'm looking for an algorithm that generates all cartesian products for a list of sets, but skips tuples that are just rotations ...
I have a Cartesian mesh in $d$ dimensions, and I would like to enumerate all the subcells of a given hexahedral cell. If I am just enumerating the vertices of a cell (or cells that contain a vertex) I ...