sol10

# sol10 - Introduction to Algorithms CS 482 Spring 2008...

This preview shows pages 1–2. Sign up to view the full content.

Introduction to Algorithms Solution Set 9 CS 482, Spring 2008 (1) There are many correct solutions; here is one. The graph has two vertices s, t and n triples of vertices ( u i , v i , w i ) n i =1 , for a total of 3 n + 2 vertices. There are 5 n edges, specified as follows. For all i , the graph contains edges ( s, u i ) , ( u i , v i ) , ( v i , t ) , ( u i , w i ) , ( w i , t ) . The subgraph consisting of vertices s, t, u i , v i , w i and the five edges between them will be denoted by G i . The unique minimum s - t cut is the one that separates s from all other vertices. This cut survives the analogue of Karger’s algorithm if and only if none of the edges ( s, u i ) is ever contracted. For i = 1 , 2 , . . . , n , let E i denote the event: “the algorithm picks edge ( s, u i ) before it picks any other edge of G i .” We observe the following facts. 1. Pr( E i ) = 1 / 5 . 2. The events {E i | i = 1 , 2 , . . . , n } are mutually independent. 3. The algorithm succeeds only if none of the events E i occurs. (Note: we are not saying that the algorithm is guaranteed to succeed if none of the events E i occurs. We are only saying

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

View Full Document
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