in both directions). The graph is fully-connected where the edge ei,j connecting any two vertices vi and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to UN (the destination). Assume that all edges have different values, and e₁,N has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.

in both directions). The graph is fully-connected where the edge ei,j connecting any two vertices vi and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to UN (the destination). Assume that all edges have different values, and e₁,N has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed
in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj
is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the
source) to VN (the destination).
...
Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the
source and destination have the largest straight-line distance. Compare the lists of explored vertices
when we run the uniform-cost search and the A* search for this problem.
Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to
start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs
satisfy the conditions in the question.

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Step 1: Optimal Path Discovery in a Fully-Connected Undirected Graph- Straight-Line Distances and Edge Value

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Step 2: Uniform-Cost Search (UCS):

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Step 3: A* Search:

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Step 4: Comparison of Explored Vertices:

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