# Questions tagged [approximation]

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

577 questions
Filter by
Sorted by
Tagged with
75 views

### Throughput measure

I have to implement a limitation algorithm in order to avoid to reach a throughput limit imposed by the service I'm interacting with. The limit is specified as «N request over 1 day» where N is of ...
882 views

### $1+\epsilon$ approximation for inapproximable problems

I am currently confused by the following situation: 1) The metric $k$-center problem is inapproximable in polynomial time within $2-\epsilon$ unless $P=NP$. 2) The metric $k$-center problem can ...
10k views

### Difference between heuristic and approximation algorithm?

i have a problem regarding the following situation. I have two arrays of numbers like this: ...
343 views

### Hardness of approximating 0-1 integer programs

Given a $0,1$ (binary) integer program of the form:  \begin{array}{lll} \text{min} & f(x) & \\ \text{s.t.} & A x = b \\ & x_i \ge 0 & \quad \forall i\\ & x_i \in \{0,1\} &...
392 views

### Implications of truncation of numbers when converted into binary

I have been posed with a question whereby a computer truncates numbers to x number of digits. Due to this, if this computer is trying to store a decimal number which has a binary equivalent greater ...
931 views

### What does big O mean as a term of an approximation ratio?

I'm trying to understand the approximation ratio for the Kenyon-Remila algorithm for the 2D cutting stock problem. The ratio in question is $(1 + \varepsilon) \text{Opt}(L) + O(1/\varepsilon^2)$. ... 240 views

### Find $\epsilon'$ s.t $L_\epsilon$ is $\mathsf{NP}$-hard for any $\epsilon<\epsilon'$

Let $L_\epsilon$ be the language of all $2$-CNF formulas $\varphi$, such that at least $(\frac{1}{2}+\epsilon)$ of $\varphi$'s clauses can be satisfied. I need to prove that there exists $\epsilon'$ ...
146 views

### Show that approximation ratio for a convex hull algorithm is $\pi/2$

Facts: n points in the plane, each has one of k colors, all k colors are represented. Problem: You wish to select k points, one of each color, such that the perimeter of the convex hull is as small ...
1 vote
198 views

458 views

### In s-t directed graph, how to find many small cuts?

Solving the maximum flow problem yields one qualified minimal cut. But I want several (maybe hundreds) small cuts as candidates. The cuts don't have to be minimum cuts, as long as they are small (in ...
1k views

### Weighted Maximum 3-DIMENSIONAL-MATCHING with restricted weights (Approx Algo)

If the weights of the weighted 3-DIMENSIONAL-MATCHING problem are restricted to let's say, 1 and 2, is there a possibility to reduce this case to the unweighted 3-DIMENSIONAL-MATCHING problem? (...
540 views

### Approximate minimum-weighted tree decomposition on complete graphs

Say I have a weighted undirected complete graph $G = (V, E)$. Each edge $e = (u, v, w)$ is assigned with a positive weight $w$. I want to calculate the minimum-weighted $(d, h)$-tree-decomposition. By ...
899 views

### Approximation algorithm for TSP variant, fixed start and end anywhere but starting point + multiple visits at each vertex ALLOWED

NOTE: Due to the fact that the trip does not end at the same place it started and also the fact that every point can be visited more than once as long as I still visit all of them, this is not really ...
683 views

### What is the name of this logistic variant of TSP?

I have a logistic problem that can be seen as a variant of $\text{TSP}$. It is so natural, I'm sure it has been studied in Operations research or something similar. Here's one way of looking at the ...
5k views

### Decision problems vs "real" problems that aren't yes-or-no

I read in many places that some problems are difficult to approximate (it is NP-hard to approximate them). But approximation is not a decision problem: the answer is a real number and not Yes or No. ...