All Questions
Tagged with packing-and-covering combinatorial-optimization
7 questions
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Optimal covering trails for every $k$-dimensional cubic lattice $\mathbb{N}^k := \{(x_1, x_2, \dots, x_n) : x_i \in \mathbb{N} \wedge n \geq 3\}$
After a dozen years spent investigating this particular class of problems, I finally give up and I wish to ask you if any improvement is achievable from here on.
The general problem is as follows:
Let ...
- 1,451
3
votes
1
answer
406
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Electricity division and bin packing
In the electricity division problem, there is a powerhouse that supplies $s$ kilowatt of electricity. There are $n$ households. The connection size of household $i$ is $d_i$.
The problem is that $s &...
- 3,549
0
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1
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182
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A variation of Set Cover
Suppose we have $n$ sets $\{S_i\}_{i=1}^n$, each containing exactly $k$ of the numbers from $1,...,n$. The union of all these sets will cover $1,...,n$. We know $i \in S_i$ for all $i$. We need to ...
- 1
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Dual equivalence of minimum feedback-vertex sets and cycle packing
it is known that the duals of feedback-set problems are set-packing problems; in the context of digraphs the feedback set are either a minimal set of vertices or edges that hit every oriented cycle; ...
- 13.2k
2
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1
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138
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Generating short Hamilton cycles from complete graphs
Let $G(V,E)$ be a complete symmetric graph without self-loops or parallel edges; depending on the context the edges may however be interpreted as a pair of antiparallel arcs of equal weight.
A vertex ...
- 13.2k
2
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2
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279
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Combinatorial optimization problem with interdependent constraints on points in $[0,1]$
We are given a set $S$ of $n$ real numbers in $[0,1]$, with $0,1\in S$, and a value $\alpha\in(0,1/2)$. For each ordered triplet $(i,j,k)$ of values contained in $S$ (with $i\le j \le k$), we define ...
- 1,677
5
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199
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Existence of a honeycomb composed by nearly-hyperspherical $d$-dimensional cells having the same shape and size
Let $\mathcal{H}$ the class of all honeycombs composed by $d$-dimensional cells $C$ having all the same shape and size in a $d$-dimensional space $\mathcal{S}$.
Let $s(C)$ and $\ell(C)$ be ...
- 1,677