Algorithm

In: Computers and Technology

Submitted By zhangiou0
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Design and Analysis of Computer Algorithm Assignment 2
Name: Boyu Zhang UTD-ID: 2021226566 Email:bxz140830@utdallas.edu

Contents
Problem 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Problem 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Problem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Problem 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Problem 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Problem 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Problem 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Problem 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Problem1 This problem can solution by Dial’s algorithm in the lesson six. We can set up W+2 buckets with the labels of 0, 1, …, W, . Then we carry out the following steps: (a). Initial the buckets with node S be in the bucket 0 and all other nodes be in the bucket . (b). then select the node with the minimum temporary distance label. For the first time, it should be the source node S in the bucket 0. (c). Update the buckets information. Then some node should be moved from the bucket  to the corresponding distance bucket. (d). Remove the selected node from the bucket. Then repeat step 2 and 3 until there is no non-empty bucket. Therefore we can compute the shortest paths from source vertexs in O(W|V|+|E|). Because the extract part’s step during the Dijkstra's algorithm takes O(W|V|) time while the decreasing operation still takes O(E) time.

Problem 2 Bottleneck Path Problem algorithm for directed graphs

2

1: INPUT: A directed graph G = (V, E) with m = |E| and edge weights de ∈D for all edge e∈E, source and…...

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