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Results tagged with oc.optimization-and-control
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user 2233
Operations research, linear programming, control theory, systems theory, optimal control, game theory
2
votes
A certain instance of the Set Covering problem
For the variant that $\mathcal{P}$ consists of all paths, the problem is equivalent to minimum vertex cover, and hence is NP-complete. To see this, I assume that single vertices do not count as paths …
- 32.1k
3
votes
Is the max of two supermodular functions supermodular?
I think the answer is no. Let $f$ be a supermodular, non-negative and increasing (in both arguments) function satisfying $f(0,0)=1, f(0,1)=2, f(1,0)=3$, and $f(1,1)=4.5$. Let $g$ be defined as $g(x, …
- 32.1k
4
votes
a different algebra/representation for convex sets
This question is a bit vague, but you may be looking for Motzkin's decomposition theorem. This theorem says that any polyhedral convex set can be expressed as the Minkowski sum of a polytope and a po …
- 32.1k
1
vote
Accepted
Connected graphs $G$ with $\delta(G) > 1$ and long minimum size roundtrips
The answer is $2$. To see this, let $G$ be the graph which consists of two triangles connected by a path with $k-4$ vertices. Then $G$ has $k$ vertices and the length of a shortest roundtrip is $2k- …
- 32.1k
6
votes
Book for matroid polytopes
Matroid polytopes are a standard topic in the field of combinatorial optimization, and as such I would recommend the beautiful text Combinatorial Optimization - Polyhedra and Efficiency by Lex Schrijv …
- 32.1k
11
votes
Fairest way to choose gifts
Here's an idea. For any partition $(A,B)$ of $[2n]$, where $|A|=|B|=n$, we can ask each child if they prefer $A$ or $B$. If one prefers $A$ and the other prefers $B$, then we are done. Otherwise, t …
- 32.1k