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Prelim1_q3sol

Prelim1_q3sol - 3(30 Consider a n u ndirected g raph G =(V...

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3. (30) Consider an undirected graph G = (V, E), where each undirected edge {i,j} has a corre- sponding cost c{ i, j}, which is an input to the minimum spanning tree problem. Suppose that V {I, 2, ... , 20}. You have already computed a minimum spanning tree in the graph G, but have lost part of the answer. You still know all of the edges with both endpoints among the nodes {I, 2, ... , 10} (there are k of them). You also still know all of the edges with both endpoints among the nodes {ll, 12, ... ,20} (there are C of them). What you have lost are all of the edges that have one endpoint among the nodes {I, 2, ... , 1O} and one endpoint among the nodes {ll, 12, ... , 20} . (a) (15) How many edges have you los~~Hint: how many edges are there in the minimum spanning tree?) A ItA S T "Uob 1i.:;'6'" \ -:: 1,0-1 ~ (9 t.O'jt'!l. We. .,.",., ..... k +1 eJ.j~ 1. C We need tq-~ .... J r-1&lrL (b) (15) Suppose that the following table gives a complete list of all of the edges in G with one endpoint in {I, 2, ... ,10} and one endpoint in {ll, 12, ... ,20}. Furthermore, suppose that k C = 9. Explain how you can use this information to recompute the missing part of the minimum spanning tree. (Once again please note that what is asked for here is the explanation, not just the answer.) Justify your ans·wer as completely as possible. {i,j} c{i,j} {1,13}
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