CSE331 Lecture 27

# CSE331 Lecture 27 - Lecture 27 CSE 331 Nov 2 2010 Online...

This preview shows pages 1–9. Sign up to view the full content.

Lecture 27 CSE 331 Nov 2, 2010

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Online Office Hr @ 10:00- 10:30pm
Follow the collaboration rules Write down names of your collaborators Collaboration is only until the proof idea stage Any deviations HW 7 onwards would be considered cheating

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Cut Property Lemma for MSTs S S V \ S V \ S Cheapest crossing edge is in all MSTs Condition: S and V\S are non-empty Assumption: All edge costs are distinct
S S V \ S V \ S Optimality of Kruskal’s Algorithm Input: G=(V,E) , c e > 0 for every e in E T = Ø Sort edges in increasing order of their cost Consider edges in sorted order If an edge can be added to T without adding a cycle then add it to T S S Nodes connected to red in (V,T) Nodes connected to red in (V,T) S is non-empty V\S is non-empty First crossing edge considered

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Is (V,T) a spanning tree? No cycles by design Just need to show that (V,T) is connected S’ S’ V \ S’ V \ S’ No edges here No edges here G is disconnected! G is disconnected!
Cut Property Lemma for MSTs S S V \ S V \ S Cheapest crossing edge is in all MSTs Condition: S and V\S are non-empty

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Optimality of Prim’s algorithm Input: G=(V,E) , c e > 0 for every e in E S = {s}, T = Ø While S
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern