Your Practice Set – Applications and Interpretation for IBDP Mathematics
2 . This question aims at investigate an urban planning problem involving Voronoi diagrams and graph theory .
There are four housing estates P , Q , R and S in a town . The diagram below shows the Voronoi diagram of the four housing estates , where 1 unit represents 100 m . The points
A � 5 , 11� � � and B ( 5 , 7 ) are the intersections of the boundaries of Voronoi cells . BC and � 3 �
AD intersect the line x � 10 at C and D respectively .
The town can be modelled by the region in the coordinate plane where 0 �x � 10 and
0 � y � 10 .
In order to minimize the noise pollution level due to traffic , the urban planner of the town decides to build highways at the location which are as far as possible from the housing estates , covering all edges of the Voronoi diagram and the external boundaries of the town .
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