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Computer Science 170 - Fall 1994 - Vazirani - Midterm 2

# Computer Science 170 - Fall 1994 - Vazirani - Midterm 2 -...

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CS170 , Midterm #2, Fall 1994 CS170, Fall 1994 Midterm #2 Professor Vazirani There are 4 independent problems of equal weight. You need to discard one problem of your choice and do the other three. You will be graded on these three. (If you turn in something for all problems, only the first three will be graded) When using material from lecture, textbook or discussion session, you do not need to repeat it entirely. It is sufficient to refer to it clearly. Please start each new problem on a new sheet of paper. Write your name on each sheet of paper. On the first page, write you ID number and which section you are enrolled in (AM or PM) (1 point) Problem #1 - Dynamic Minimum Spanning Tree (35 points) Let G = V(V,E) be an undirected graph, with a weight function w(e) > 0 for each edge e < E. Let T be a Minimum Spanning Tree (MST) of G for this weight function. We consider the problem which takes as input a minimum spanning tree T of G and a request "Decrease the weight of edge e i down to w'(e i )", where w'(e i ) < w(e i ), and outputs the new minimum spanning tree T' of G with this new wieght. 1.1 Example. (5 points) For example, consider the graph G below. Draw a minimum spanning tree T of G. If the request is "Change teh weight of edge {b, d} from 10 to 3", then draw the new MST T'.

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