# Questions tagged [combinatorics]

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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### Graph optimization for parallel processing

Consider the following example structure of overlapping images marked A,B,C,D. The possible overlaps are marked by gray color: The structure can be represented by a weighted undirected graph (images ...
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### Integer partition algorithms

I am familiar with and have written MathCad algorithms for the partition functions π(π,π),which gives the number of ways of partitioning π into π parts, π(π,π), which gives the number of ways ...
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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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### maximum eigenvalue across subsamples

I have an $N$-dimensional vector of data, say $X_{t}$, with $1 \leq t \leq T$. Of this vector $X_{t}$, I want to consider vectors, say $X_{t}^{b}$, which are $m$-dimensional combinations of elements ...
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### GPGPU/FPGA programming for Combinatorial Analysis

Recently, I have taken an interest in performing combinatorial analysis for the game of 21 (blackjack) and attempted to use my AMD APU to try and thread the program via the 4 cores on the chip. ...
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A consistency notion in constraint programming: Let $P = (X, D, C)$ be a CSP. Given a set of variables $Y \subseteq X$ with $|Y| = k -1$, a locally consistent instantiation $I$ on $Y$ is $k$-...
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### What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money π to spend over π different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
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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 ...
28 views

### 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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### Is this problem statement good for a GPU?

I am used to using GPU hardware for large scale matrix operations and vectorizing mathematical operations on a continuous space which has been discretized for numerical computation, but this is a ...
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### Which algorithm is capable of solving a combinatorial optimization problem like this?

The problem I have at hand is a regression problem where each of $p$ inputs, $x_1, x_2, x_3, \cdots, x_p$, needs to undergo a variable transformation using one of $q$ basis functions from a set of ...