Problem 1: The Cell Tower Due to the current pandemic, people use the Internet and other means of communication extensively. This overloads the current cellular network. Therefore, the responsible telecom company proposed to build new cell towers in areas with high loads. The new towers would increase the network availability in case of a failure in the original tower. Nevertheless, because these towers require a minimum height, the locations of the new cell towers are limited to particular buildings. You are required to help the telecom company to make their decision regarding where to build the new tower in a particular area. Input: you are given a list S of tuples (xi, Yi) indicating the locations, with cartesian coordinates, of candidate buildings. Example: [(0,0),(1,3), .. ] Output: return the tuple t = (xk, Yk) E S that indicates the building location above which we will build the cell tower Criteria: i) choose the building that has the minimum average-distance between it and the other candidate buildings ii) choose the building that has the minimum marimum-distance between it and the other candidate buildings Requirements: For each criteria, make sure to submit the following A) develop a python function that outputs the chosen location depending on the candidate buildings according to the criteria. B) empirically, test your functions while increasing the number of candidate buildings. C) show the complexity analysis of your developed functions, theoretically.

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Problem 1: The Cell Tower
Due to the current pandemic, people use the Internet and other means of communication
extensively. This overloads the current cellular network. Therefore, the responsible
telecom company proposed to build new cell towers in areas with high loads. The new
towers would increase the network availability in case of a failure in the original tower.
Nevertheless, because these towers require a minimum height, the locations of the new
cell towers are limited to particular buildings. You are required to help the telecom
company to make their decision regarding where to build the new tower in a particular
area.
Input:
you are given a list S of tuples (xi, Yi) indicating the locations, with cartesian
coordinates, of candidate buildings. Example: [(0,0),(1,3),
Output:
return the tuple t = (xk, Yk) E S that indicates the building location above which
we will build the cell tower
Criteria:
i) choose the building that has the minimum average-distance between it and the
other candidate buildings
ii) choose the building that has the minimum maximum-distance between it and the
other candidate buildings
Requirements: For each criteria, make sure to submit the following
A) develop a python function that outputs the chosen location depending on the
candidate buildings according to the criteria.
B) empirically, test your functions while increasing the number of candidate buildings.
C) show the complexity analysis of your developed functions, theoretically.
Transcribed Image Text:Problem 1: The Cell Tower Due to the current pandemic, people use the Internet and other means of communication extensively. This overloads the current cellular network. Therefore, the responsible telecom company proposed to build new cell towers in areas with high loads. The new towers would increase the network availability in case of a failure in the original tower. Nevertheless, because these towers require a minimum height, the locations of the new cell towers are limited to particular buildings. You are required to help the telecom company to make their decision regarding where to build the new tower in a particular area. Input: you are given a list S of tuples (xi, Yi) indicating the locations, with cartesian coordinates, of candidate buildings. Example: [(0,0),(1,3), Output: return the tuple t = (xk, Yk) E S that indicates the building location above which we will build the cell tower Criteria: i) choose the building that has the minimum average-distance between it and the other candidate buildings ii) choose the building that has the minimum maximum-distance between it and the other candidate buildings Requirements: For each criteria, make sure to submit the following A) develop a python function that outputs the chosen location depending on the candidate buildings according to the criteria. B) empirically, test your functions while increasing the number of candidate buildings. C) show the complexity analysis of your developed functions, theoretically.
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