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# a10 - MATH239 Assignment 10 Due July 22(by Noon 1(10 points...

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MATH239 Assignment 10 Due: July 22 (by Noon) 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, determine the sets X 0 , X , and Y from the XY construction. Find either an M -augmenting path or cover C with | C | = | M | . ii. Let M = { 1 a, 2 c, 5 d, 4 b, 6 f, 8 i, 9 h, 7 e } . Using the bipartite matching algorithm, deter- mine the sets X 0 , X , and Y from the XY construction. Find either an M -augmenting path or cover C with | C | = | M | . 2. (10 points) An n × n matrix P , with entries in { 0 , 1 } , is a permutation matrix if each row and each column contains exactly one 1. Hence the identity matrix is a permutation matrix and every permutation matrix can be obtained from the identity matrix by permuting its rows and columns. i. Write the following matrix as the sum of permutation matrices. A = 2 0 1 0 0 1 1 1 1 0 1 1 0 2 0 1 .

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a10 - MATH239 Assignment 10 Due July 22(by Noon 1(10 points...

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