Transcript 초간단 알고리즘 정리

초간단 알고리즘 정리
Independent Set
Clique
Vertex Cover
Set Cover
Seikwon@KAIST
Independent Set 이란?
• 그래프에서 vertext간 edge가 이어져 있지 않은 Set
Independent Set (Size 3)
Clique 란?
• 그래프에서 vertext간 edge가 서로 이어져 있는 Set
Clique (size 3)
Reducing Independent Set to Clique
Independent Set
in the Graph
Complimentary of
Independent Graph
Independent Set In
Complimentary of
Independent Graph
= Clique
Actual Clique
in the Graph
Clique is as hard as Independent Set
Vertex Cover란?
• Vertex들을 선택 했을때 전체 Edge를 다 커버할 수 있다.
Vertex Cover
Independent Set to Vertex Cover
+
Independent Set
=
Vertex Cover
-
=
Independent Set
Vertex Cover
Set Cover란?
• Together is entire Universe
Let U = {1,2,3,4,5,6,7}
S1 = {3,7}
S2 = {2,4}
S3 = {3,4,5}
S4 = {5,6}
S5 = {1}
S6 = {1,2,6,7}
+ = {1,2,3,4,5,6,7} = Entire Universe.
So S3, S6 are Set Cover
Vertex Cover to Set Cover
• Set Cover를 그래프로 그려보자
Let U = {1,2,3,4,5,6,7}
S3
S1 = {3,7}
3
S2 = {2,4}
S3 = {3,4,5}
S4 = {5,6}
S5 = {1}
S1
5
4
S3, S6은 Set Cover
As well as Vertex Cover
S4
S2
S6 = {1,2,6,7}
7
2
S6
6
1
S5