hw05 - u to v or from v to u or both u and v may lie on a...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
CS170 - Spring 2010 Problem Set 5 Out: Feb 28, 2010 Due: Mar 5, 2010, 4pm Please write your name, your student ID number, course name (CS170), homework number (this is HW#1), your TA’s name and your section number on the first page of all of your homeworks, and staple all the pages together. Please put your name, CS170 and homework number on all the pages (in case they get separated). Note DPV = Dasgupta, Papadimitriou, Vazirani refers to the textbook. So DPV 2.5 refers to Problem 5 in Chapter 2 of DPV. 1. DPV 4.1, 4.2, 4.4, 4.5, 4.13, 4.19, 4.21 2. A directed graph G = ( V, E ) is called semiconnected if for every pair of distinct vertices u and v there is either a path from
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: u to v or from v to u , or both ( u and v may lie on a cycle). Show that G is semiconnected if and only if the DAG formed by G ’s strongly connected components has a unique topologically sorted order, i.e. there is a unique way to order the DAG vertices v 1 , v 2 , . . . , v n such that any edge ( v i , v j ) satisfies i < j . Hint: Let ˜ G denote the DAG of strongly connected components of G . Show that G is semiconnected if and only if ˜ G has the following property: If v i and v i +1 are consecutive vertices in a topological sort of ˜ G , then the edge ( v i , v i +1 ) exists in ˜ G ....
View Full 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