Math 103, Section 11, Friday, April 15, 2011
Homework for Chapter 5 is due on Friday, April 15, 5 minutes before midnight.
Please do Exercises (
on pages 193-196
)
20,26,30,34,38,42 and 46
and upload
to Sakai.
Homework for Chapter 6 will be discussed in class and not submitted to Sakai.
Exercises (on pages 229-232) 24,26,30,32,40,46
There will be a quiz on Chapter 6 on Tuesday, April 26.
Homework for Friday, April 15. Page 229 Exercises 23,25,29
Chapter 6 The Mathematics of Touring
Hamilton Paths and Hamilton Circuits and The Traveling Salesman Problem
Graph model of a traveling salesman problem
Sites
vertices of the graph
Costs
weights of the edges
Tour
Hamilton circuit
Optimal tour
Hamilton circuit of least total weight
A
tour
is a Hamilton circuit of the graph and an
optimal tour
is the Hamilton circuit of
least total weight.
Strategies for solving Traveling Salesman Problems (TSPs)
We will learn:
1. Exhaustive Search. Also called the Brute-Force Method.
2. Nearest-Neighbor Algorithm
3. Repetitive Nearest-Neighbor Algorithm
4. The Cheapest-Link Algorithm
Table 2 completed
Starting
vertex
Route
Route
starting with
A
Cost of route
A
A,C,E,D,B,A
A,C,E,D,B,A
$773
B
B,C,A,E,D,B
A,E,D,B,C,A
$722
C
C,A,E,D,B,C
A,E,D,B,C,A
$722
D
D,B,C,A,E,D
A,E,D,B,C,A
$722
E
E,C,A,D,B,E
A,D,B,E,C,A
$741