# Questions tagged [approximation-hardness]

Hardness of approximation, aka inapproximability.

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### Large CLIQUE approximation

I am interested in algorithms to identify large cliques in graphs where the largest clique is a large fraction (definitely greater than half, perhaps as great as 4/5) of the total number of vertices. ...
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### For what parameters is minimum distance hard?

It has been shown by Vardy that minimum distance of a code is NP-hard (see Alexander Vardy, “The Intractability of Computing the Minimum Distance of a Code,” IEEE Trans. Inf. Thy., Vol. 43 pp. 1757--...
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### Hardness of Approximation of Continuous Metric k-Median

First let me describe the metric $k$-median problem. Definition (Metric $k$-Median): Given a set $C$ of clients and a set $L$ of facility locations defined over a distance metric $d$. Open a set $F$ ...
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### Balanced and general $MAXkSAT$ known approximation results and bounds from $UGC$

$MAX2SAT$ has a $0.9401$ to $0.9402$ approximation algorithm which is conjectured to be optimal by $UGC$ while there is a balanced $MAX2SAT$ bound of $0.943$ approximation which is conjectured to be ...
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### Why does Dinur's proof of the PCP theorem fail to work for unique games?

What is the critical step where things go wrong if one attempts to use Dinur's proof the PCP theorem to prove the unique games conjecture by starting from a unique label cover instance and doing gap ...
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### What does it mean by the statement: "a problem is hard to approximate "?

In most of the research papers that I have read so far, I often come across the statement of the following form: "the problem is hard to approximate within any factor smaller than some constant&...
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### Best approximations of Minimum Dominating Sets in chordal graphs

I am searching results and papers related to the (in)approximability of the Minimum Dominating Set problem in chordal graphs. In particular, what is the best approximation ratio achievable in polytime ...
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### polytime approximability of directed multicut

Does anyone know how well directed multicut can be approximated in planar and minor free graphs? Also any survey of approximability of directed multicut and multicut in various graph classes would be ...
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### Where to find info on (polytime) approximability of various discrete optimization problems?

Where to find info on (polytime) approximability of various discrete optimization problems? Sorry if this is stupid,but is there a site or reference that keeps up to date info on approximability of ...
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### Good Survey paper for k-means/k-median/k-center/facility-location

I have stated 4 problems in the Question title. All these problems are closely related and are studied in various variations. For example: Space: Euclidean/metric/discrete/continuous/non-metric/2-...
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### Is the following graph optimization problem approximable within a constant factor?

Let $G=(V,E)$ be an undirected graph, and let $\pi$ be a permutation of the vertices in $V$. For a node $v\in V$, we denote by $\text{pred}_{\pi}(v)$ (respectively $\text{succ}_{\pi}(v)$) the set of ...