# Questions tagged [approximation]

Questions about algorithms that solve problems up to some bounded error.

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### Max matching algorithm lemma approximation algorithm

We have this algorithm which is supposed to find max matchings. ...
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### Special case of single vehicle routing

I have a metric space $(V,d)$ described by a tree $T$. And I have $k$ pair of vertices $\{s_i,t_i\}$ ($i \in [k]$) s.t. each of the vertices $s_i$ and $t_i$ are leaves of $T$. There is a car at one ...
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### approximation ratio of TSP problem where the weights are bounded by an inequality

Consider a variant of the TSP problem where the cost function $c$ is not only symmetric but also satisfies $c(u, v) ≤ 2c(u, w) + c(w, v)$ for arbitrary vertices $u, v, w ∈ V$ . Give a polynomial time ...
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### Is $\frac{opt}{c}(1-\epsilon)$ for some constant c >0 considered a PTAS?

So I am studying PTAS algorithms. For a maximazation problem the difinition says that an algorithm that has value A , is a ptas if : $A \geq opt(1-\epsilon) \; ,\forall \epsilon > 0$ (and I guess ...
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### Embedding from $L^\infty$ space to $L^2$ space

I have a set $X$ of $n$ points in a $poly(n)$-dimensional $L^\infty$ space. Does there exist a way to map the points into $poly(n)$-dimensional $L^2$ space so that the distances between points in $X$ ...
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### What is an O(n)-approximation?

I see the following notations used: $O(1)$-approximation $O(n)$-approximation $\Omega(n)$-approximation Can someone please explain what they mean? I know what an approximation is with a normal ...
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