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Results tagged with combinatorial-optimization
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user 46140
Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.
20
votes
Accepted
Splitting the integers from $1$ to $2n$ into two sets with products as close as possible
Original question
Is this sequence strictly increasing?
No.
n difference smaller half
16 16753029012720 [3, 5, 6, 7, 9, 10, 11, 13, 15, 18, 19, 21, 25, 27, 29, 30]
17 10176199188480 [4, 6, 7, 8 …
- 7,226
1
vote
Maximize this score function on a directed tree
If $a \to b$ then $s(b) \ge s(a)$, so an $a$ which maximises $s(a)$ subject to $\operatorname{dep} a \le N$ has $\operatorname{dep} a = N$.
If $k_1 < k_2$ and $a_{k_1} < a_{k_2}$ then the word obtaine …
- 7,226
1
vote
Accepted
Mapping problem reminiscent of Mastermind
Since $S$ is finite, we can label its elements $s_1, s_2, \ldots, s_n$. Then take as query sets $S_1 = \{ s_i \mid i \,\&\, 1 = 1 \}$ where $\&$ represents bitwise conjunction; $S_2 = \{ s_i \mid i \, …
- 7,226
1
vote
Integer linear constraint(s) for y= x1 XOR x2
If we consider the cube $0 \le x_1, x_2, y \le 1$ then the eight possible Boolean assignments to $x_1, x_2, y$ are the vertices of the cube. We can mark an assignment $x_1 = a, x_2 = b, y = c$ as ille …
- 7,226
2
votes
Accepted
Combinatorial graph optimization problem on integer adjacency matrices
Consider $$M_{i,j} = \begin{cases} 1 & \textrm{if } i \equiv j \pmod 2 \\ N & \textrm{if } i \not\equiv j \pmod 2\end{cases}$$ where $N > 1$. Then
$$\min(M_{i,k}, M_{k,j}) = \begin{cases} 1 & \textrm{ …
- 7,226