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

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

View Full Document Right Arrow Icon
Lecture 27 CSE 331 Nov 2, 2010
Image of page 1

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

View Full Document Right Arrow Icon
Online Office Hr @ 10:00- 10:30pm
Image of page 2
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
Image of page 3

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

View Full Document Right Arrow Icon
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
Image of page 4
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
Image of page 5

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

View Full Document Right Arrow Icon
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!
Image of page 6
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
Image of page 7

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

View Full Document Right Arrow Icon
Optimality of Prim’s algorithm Input: G=(V,E) , c e > 0 for every e in E S = {s}, T = Ø While S
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern