Unformatted text preview: algorithm, assume that vertices are considered in alphabetic order. In Kruskal’s algorithm, if two edges are of the same costs, the one which has smaller end vertices (in the alphabetical order) should be considered ±rst. Show intermediate steps in executing the algorithm. a b c d e f g h i 1 3 7 5 4 3 5 7 8 2 4 6 8 4 1 Figure 1: Problem 4 Assume n programs of length l 1 , l 2 , · · · , l n are to be stored on a tape. Program i is to be retrieved with frequency f i . If the program are stored in the order of i 1 , i 2 , · · · , i n , the expected retrieval time (ERT) is ∑ j ( f i j ∑ j k =1 l i k ) ∑ f i a. Show that storing programs in nondecreasing order of l i does not necessarily minimize ERT. b. Show that storing programs in nonincreasing order of f i does not necessarily minimize ERT. c. Show that storing programs in nonincreasing order of f i /l i does minimize ERT. 1...
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 Winter '08
 SURI
 Computer Science, Algorithms, Graph Theory, Data Structures, shortest path, Prim, connected undirected graph, Kruskal, smaller end vertices

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