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Results tagged with combinatorial-optimization
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user 43954
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.
10
votes
Accepted
Desargues ten point configuration $D_{10}$ in LaTeX
This example shows that $s\le 2$ and for this $s$, $c\le 3$.
Note that we are lucky with the latter, because there is a configuration for which every combinatorially equivalent realization has at lea …
- 5,409
1
vote
Accepted
Electricity division and bin packing
Let us show that a required $k$-times bin-packing exists for some $k\le n^{n/2}$.
Let $V=\{(v_1,\dots,v_n)\in\{0,1\}^n:\sum_{i=1}^n d_iv_i\le s\}$ be the set of all admissible "bin packings". Then the …
- 5,409
0
votes
Tighter lower bound of the lower triangular sum of an arbitrary Latin square
For each $1\le i\le n-1$ the sum of numbers of $i$-th column of the lower triangle $\Delta$ below the main diagonal is at least $1+\dots+i=i(i+1)/2$. Thus the sum of all numbers in $\Delta$ is at leas …
- 5,409
0
votes
Transforming an optimization problem to maxmin formulation
This answer is partial.
We assume that all $a_i$ are non-negative. Put $A=\tfrac 1m \sum a_i$ and $A_j=\sum_{i\in S_j} a_i$. We want to maximize $\Pi=\prod A_j$. But by AM-GM inequality, $P^{1/m}\le …
- 5,409