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Unformatted text preview: Homework #6 Due Date: Monday, November 22nd, start of class 1. Napoleon Bonaparte, the great French Emperor and ruthless military genius 1 seeks to establish efficient administrative communication between Paris and n other provinces in France through one-way broadcast messages from Paris along pre-specified paths. There are k different languages spoken across the French empire, and thus a lot of consecutive translations may need to happen along the way to a remote province when a message is sent. Each province speaks just one of k languages. Napoleons messengers carry message scrolls from Paris (in French) along a graph G = ( V,E ) of roads and sailing routes. Each message scroll has a specific destination t . Only three-way intersections are present, which means that at each intersection the messenger has exactly 2 choices (since one of the paths leads back the way they came). At each intersection lies a checkpost where scrolls come and the message is translated to the language required of the next node in the path. The emperor has a k k matrix, C, of positive numbers for the cost C ( i,j ) of translating from language i to language j . The translation costs in the matrix are not necessarily symmetric.....
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