assignment4_sol

# assignment4_sol - CSIS 0250B Design and Analysis of...

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

CSIS 0250B Design and Analysis of Algorithms Assignment 4 Sampled Solution 1. As matching M of G with n - 1 edges are given, we have 1 vertex on each side of the bipartite graph that are not matched. We construct a directed graph G 0 from G . For each edge e ( u, v ) E - M , we create a directed edge e ( u, v ) on G 0 . For each edge e ( u, v ) M , we create a directed edge e ( v, u ). WLOG, let the unmatched vertex on the left hand side be s and the one on the right hand side be t . We apply BFS/DFS on G 0 starting with the vertex s and find a path from s to t . If such path exists, we conclude that there exists a perfect matching; otherwise we conclude there does not exist one. Correctness We try to augment the matching like the Maximum Flow Algo- rithm does. The G 0 is in fact a reconstruct of the residual network we would use to solve the bipartite problem on G . If there exists a perfect matching, we should be able to find an augmenting path that increases the current flow by 1, i.e. the path from s to t .

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