초간단 알고리즘 정리 Independent Set Clique Vertex Cover Set Cover

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Presentation transcript:

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 Complimentary of Independent Graph Independent Set in the Graph 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} So S3, S6 are Set Cover

Vertex Cover to Set Cover 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} S3 3 5 S3, S6은 Set Cover As well as Vertex Cover 4 S1 S2 S4 2 6 7 S6 S5 1