How do I find my set cover?
Table of Contents
, and the task is to find a set covering that uses the fewest sets. The decision version of set covering is NP-complete, and the optimization/search version of set cover is NP-hard….Set cover problem.
| Covering problems | Packing problems |
|---|---|
| Polygon covering | Rectangle packing |
What is approximation algorithm explain set cover problem using approximation algorithm?
Set Cover is a problem whose study has led to the development of fundamental techniques for the entire field of approximation algorithms [2]. • It is a generalization of many other important NPC problems such as vertex cover and edge cover.
What is approximation ratio of the approximate vertex cover problem?
Vertex Cover: We begin by showing that there is an approximation algorithm for vertex cover with a ratio bound of 2, that is, this algorithm will be guaranteed to find a vertex cover whose size is at most twice that of the optimum.
What is 2 approximation algorithm?
An algorithm with approximation ratio k is called a k-approximation algorithm; both algorithms above would be called 2-approximation algorithms. When the approximation ratio is close to 1, it is often more useful to look at the approximation error, which is defined as the approximation ratio minus 1.
Is set cover in P?
Set Cover is NP-Hard: There is no polynomial time solution available for this problem as the problem is a known NP-Hard problem. There is a polynomial time Greedy approximate algorithm, the greedy algorithm provides a Logn approximate algorithm.
What is a set covering model?
The set covering problem is a specific type of a discrete location model. In this model, a facility can serve all demand nodes that are within a given coverage distance Dc from the facility. The problem is the place the minimum number of facilities so as to ensure that all demand nodes can be served.
What is approximation algorithm explain with an example?
A simple example of an approximation algorithm is one for the minimum vertex cover problem, where the goal is to choose the smallest set of vertices such that every edge in the input graph contains at least one chosen vertex.
What is N approximation algorithm?
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one.
What is N approximation?
If an algorithm A guarantees to return solutions with a performance guarantee of at most r(n), then A is said to be an r(n)-approximation algorithm and has an approximation ratio of r(n). Likewise, a problem with an r(n)-approximation algorithm is said to be r(n)-approximable or have an approximation ratio of r(n).
Is set cover in NP?
Theorem: Set Cover is NP-Complete. Proof: First, we argue that Set Cover is in NP, since given a collection of sets C, a certifier can efficiently check that C indeed contains at most k elements, and that the union of all sets listed in C does include all elements from the ground set U.