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Section 16.1 Motivation

Example 16.1.1. Reducing redundancy.

You have set up your own tree-fort communication system out of tin cans and strings. (See Worked Example 15.4.11.) However, peace has broken out and your communication system is underused. To address the crippling tin-can-and-string stilts shortage, you want to dismantle as much of your network as possible without disrupting communications.
A communication network.
Figure 16.1.2. TreeFort CommNet.
Closed paths are redundant, as communication could be routed around such a path in two directions. So try to eliminate closed all paths; two possible solutions appear in Figure 16.1.3.
A communication network with redundant paths removed.
(a) One possible result of removing redundancy.
A communication network with redundant paths removed.
(b) Another possible result of removing redundancy.
Figure 16.1.3. TreeFort CommNet (after removing redundant communication paths).

Remark 16.1.4.

A more difficult modification of the above example would be to include the length of string in each communication link as a weight for that edge in the graph, and then try to determine a configuration that removes the most string from the network without disrupting communications.