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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.
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
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
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
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