# chap7sol - s,x i of capacity 2 x i,z j of capacity 1...

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CSCI 323/700 SPRING 10 SOLUTIONS FOR REVIEW PROBLEMS ON NETWORK FLOWS 1. TEXTBOOK CHAPTER 7, EXERCISE 4. The statement is false. Consider a graph G with nodes s,v,t , edges ( s,v ) and ( v,t ) with capacities 2 and 1 respectively. In the maximum ﬂow (which assigns a value of 1 to each edge), the edge ( s,v ) is not saturated. 2. TEXTBOOK CHAPTER 7, EXERCISE 20(A). Deﬁne a ﬂow network as follows: (vertices) source s , a node x i representing each balloon i , a node z i representing each condition c i and a sink t . (edges) There are edges
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Unformatted text preview: ( s,x i ) of capacity 2 , ( x i ,z j ) of capacity 1 whenever c j ∈ S i and edges ( z j ,t ) of capacity k . We then test whether the maximum s-t ﬂow has value nk . Running time. The Ford-Fulkerson algorithm to ﬁnd a maximum ﬂow has running time O ( | E | C ) where | E | is the number of edges and C is the total capacity of edges out of s . Here, we have | E | = O ( mn ) and C = 2 m , so the running time is O ( m 2 n ) ....
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## This note was uploaded on 05/22/2010 for the course CS 316 taught by Professor Stevenku during the Spring '10 term at Universidad San Martín de Porres.

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