a List the degrees of the nodes in the network. b What is the length of the shortest route that starts and finishes at P and uses every arc at least once? a Find a minimum spanning tree for the network described by the distance matrix shown.
PL E
4
b Give the total weight of the tree.
J
K
14
L
9
M
N
14
9
−
22
−
15
23
−
15
−
17
8
M
−
L
M
−
23
17
−
20
N
22
−
8
20
−
a Apply the nearest neighbour algorithm to the network in question 4, starting at node J .
SA
5
J
K
b Calculate a lower bound for the travelling salesperson problem by using the reduced network formed by removing N .
6
A cake decorator wants to mark out a design in icing. To avoid making a mess when starting and stopping icing, he wants to draw the design as a continuous route. He will achieve this by duplicating some arcs, but wants to minimise the number of nodes that are travelled through more than twice. The design is shown.
Original material © Cambridge University Press 2018