Researchers are trying to use machine learning algorithms to make redistricting more equitable and efficient. For a sample of six zones (labelled Z1-Z6), each zone can be described by at least one letter (A-F), which is a qualitative measure of that zone. One part of the algorithm is to output a potential district layout, which can only happen if each zone can be matched to exactly one letter. Consider the following descriptions for one sample of six zones: Z1 matches B or D; Z2 matches C, E, or F; Z3 matches A or F; Z4 matches B or D; Z5 matches C or F; and Z6 matches D. (a) Draw the bipartite graph that models the zones (Z1-Z6) and the letters they match (A-F).
Researchers are trying to use machine learning algorithms to make redistricting more equitable and efficient. For a sample of six zones (labelled Z1-Z6), each zone can be described by at least one letter (A-F), which is a qualitative measure of that zone. One part of the
Consider the following descriptions for one sample of six zones: Z1 matches B or D; Z2 matches C, E, or F; Z3 matches A or F; Z4 matches B or D; Z5 matches C or F; and Z6 matches D.
(a) Draw the bipartite graph that models the zones (Z1-Z6) and the letters they match (A-F).
(b) Use Hall’s theorem to determine if algorithm will be able to successfully create a district layout.
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