Consider a collection C of subsets of a nite set V . (V; C) is called a hypergraph. A hypergraph (V; C) is 3-regular if every subset in C contains exactly three elements. A subcollection M of C is matching if all subsets in M are disjoint. Show that there exists a polynomial-time 3-approximation for the maximum matching problem in 3-regular hypergraphs as follows: Given a 3-regular hypergraph, find a matching with maximum cardinality.

Explanation:

polynomial-time 3-approximation for the maximum matching problem in 3-regular hypergraphs as follows: Given a 3-regular hypergraph, find a matching with maximum cardinality.

assuming you are in the home page.

1) go to the upper right hand corner

2) click on your "profile picture"

3) go down to "edit profile"

4) it should be titled as "edit your profile", click on "profile picture"

5) choose a file

6) press "change"

you're profile picture is updated

~

only #2 represents an object at rest on a table.

in #1, there is no normal force due to the table; the object is accelerating downward.

in #3, the vertical forces are not balanced; the object is accelerating downward.

in #4, neither the vertical nor the horizontal forces are balanced. the object is accelerating upwards and to the right.