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Greedy2
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Terms in this set (20)
how to check your algorithm is correct...
a global optimum is always reach
in greedy algorithm properties, an optimization problem has optimal substructure iif ...
an optimal solution to the problem contains within it optimal solutions to subproblems.
Greedy algorithms are easily designed, but .............. of the algorithm is harder to show.
correctness
Let S be a finite set, and F a .................family of subsets of S, that is, F⊆ P(S).
we call (S,F) a matroid iif
non empty
M1) If B∈F and A ⊆ B, then A∈F. [The family F is called hereditary]
M2) If A,B∈F and |A|<|B|, then there exists x in B\A such that A∪{x} in F [This is called the exchange property]
Let M be a matrix.
Let S be the set of rows of M and F = { A | A⊆S, A is a .................}
A is linearly independent .
Let G=(V,E) be a graph. We call a graph (V,E') an induced subgraph of G if and only if ...................
its edge set E' is a subset of E.
Tell to your handsome study mate that how much do you know about spanning tree
Given a connected graph G, a spanning tree of G is an induced subgraph of G that happens to be a tree and connects all vertices of G. If the edges are weighted, then a spanning tree of G with minimum weight is called a minimum spanning tree
The picture is in page 12
if the edges are weight, the spanning tree is called a ....
minimum spaning tree
Let G=(V,E) be an undirected graph. Choose S = E and F = { A | H = (V,A) is an induced subgraph of G such that H is a forest }
Use matroid definition to prove (S,F) is a matroid
page 12 or 13
A matroid (S,F) is called ..............if it equipped with a weight function w: S->R+, i.e., all weights are nonnegative real numbers.
weighted
Weight functions of this form are sometimes called .................weight functions.
"linear"
Please write the greedy algorithm for matroids
page 15
Let M= (S,F) be a weighted matroid with weight function w. Then Greedy(M,w) returns a set in F of ....................
sorting of S is ..........
maximal weight, maximal weight.
Let M=(S,F) be a matroid. The algorithm Greedy(M,w) returns a set A in F ............................w(A).
maximizing the weight
how to find the minimal weight in matroid
use Greedy with weight function w'(a) = m-w(a) for a in A
Let M be a matrix.
Let S be the set of rows of the matrix M and F = { A | A⊆S, A is linearly independent }.
Weight function w(A)=|A|. What does Greedy((S,F),w) compute?
a basis of the vector space spanned by the rows of the matrix M.
Let G=(V,E) be an undirected connected graph.
Let S = E and F = { A | H = (S,A) is an induced subgraph of G such that H is a forest }.
Let w be a weight function on E.
Define w'(a)=m-w(a), where m>w(a), for all a in A.
.................returns a minimum spanning tree of G. This algorithm in known as Kruskal's algorithm.
Greedy((S,F), w') r
what is Kruskal's MST algorithm
Youtube
At the bottom line, matroids characterize a group of group of problems for which.....
the greedy algorithm yields an optimal solution.
Kruskals minimum spanning tree algorithm fits nicely into this framework.
Hey, you might want to understand about the Matroid more, it is quite important
...
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