sol10 - MATH239 Assignment 10 Solutions 1. (10 points)...

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

View Full Document Right Arrow Icon
Assignment 10 Solutions 1. (10 points) Consider the following bipartite graph G with bipartition ( A,B ) where A = { 1 ,..., 9 } and B = { a,b,. ..,i } . i 2 3 4 5 6 7 8 9 a b c d e f g h 1 i. Let M = { 3 a, 4 b, 6 c, 7 d, 9 h, 8 i } . Using the bipartite matching algorithm, de- termine the sets X 0 , X , and Y from the XY construction. Find either an M -augmenting path or cover C with | C | = | M | . Solution. X 0 = { 1 , 2 , 5 } . So 1 , 2 , 5 X . The following table gives the vertices in X and Y in the order added. new vertex a 3 c 6 b 4 d 7 e h 9 g f i 8 added to set Y X Y X Y X Y X Y Y X Y Y Y X predecessor 1 a 5 c 3 b 5 d 7 7 h 7 6 9 i Thus X = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } and Y = { a,b,c,d,e,f,g,h,i } . Note that g Y is M -exposed, and P = (5 ,d, 7 ,g ) is an M -augmenting path. ii. Let M = { 1 a, 2 c, 5 d, 4 b, 6 f, 8 i, 9 h, 7 e } . Using the bipartite matching algorithm, determine the sets X 0 , X , and Y from the XY construction. Find either an M -augmenting path or cover C with | C | = | M | . Solution. X 0 = { 3 } . So 3 X . The following table gives the vertices in X and Y in the order added. new vertex a b c d 1 2 4 5 added to set Y Y Y Y X X X X predecessor 3 3 3 3 a c b d Thus X = { 1 , 2 , 3 , 4 , 5 } and Y = { a,b,c,d } . Note that Y contains no M - exposed vertex. Let C
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/13/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.

Page1 / 4

sol10 - MATH239 Assignment 10 Solutions 1. (10 points)...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online