   Chapter 10.6, Problem 12ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Use Dijkstra’s algorithm for the airline route system of Figure 10.6.3 to find the shortest distance from Nashville to Minneapolis. Make a table similar to Table 10.6.1 to show the action of the algorithm.

To determine

The shortest path for the given problem using Dijkstra’s algorithm.

Explanation

Given information:

The graph of the routes allowed by Federal Aviation Authority is given as,

Calculation:

Now, calculate the shortest path from Nashville to Minneapolis using Dijkstra’s algorithm.

Let n = Nashville, S = St. Louis, Lv = Louisville, Ch = Chicago, Cn = Cincinnati, D = Detroit, Mw = Milwaukee, and Mn = Minneapolis.

 Iteration V(T) E(T) F 012345678 {N}{N}{N,Lv}{N,Lv,Cn}{N,Lv,Cn,S}{N,Lv,Cn,S,Ch}{N,Lv,Cn,S,Ch,D}{N,Lv,Cn,S,Ch,D,Mw}{N,Lv,Cn,S,Ch,D,Mw,Mn} ∅∅{{N,Lv}}{{N,Lv},{Lv,Ci}}{{N,Lv},{Lv,Ci},{Lv,S}}{{N,Lv},{Lv,Ci},{Lv,S},{Lv,Ch}}{{N,Lv},{Lv,Ci},{Lv,S},{Lv,Ch},{Lv,D}}{{N,Lv},{Lv,Ci},{Lv,S},{Lv,Ch},{Lv,D},{Ch,Mw}} {N}{Lv,Mn�

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