# hbs7(1) - 3 Let G = V E be a graph For each edge e let d e...

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CS 473 HBS 7 Spring 2009 CS 473: Undergraduate Algorithms, Spring 2009 HBS 7 1. Let G = ( V , E ) be a directed graph with non-negative capacities. Give an efficient algorithm to check whether there is a unique max-flow on G? 2. Let G = ( V , E ) be a graph and s , t V be two specific vertices of G . We call ( S , T = V \ S ) an ( s , t ) -cut if s S and t T . Moreover, it is a minimum cut if the sum of the capacities of the edges that have one endpoint in S and one endpoint in T equals the maximum ( s , t ) -flow. Show that, both intersection and union of two min-cuts is a min-cut itself.
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Unformatted text preview: 3. Let G = ( V , E ) be a graph. For each edge e let d ( e ) be a demand value attached to it. A ﬂow is feasible if it sends more than d ( e ) through e . Assume you have an oracle that is capable of solving the maximum ﬂow problem. Give efﬁcient algorithms for the following problems that call the oracle at most once. (a) Find a feasible ﬂow. (b) Find a feasible ﬂow of minimum possible value. 1...
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