Practice Network Flows (11.2.2) - Reductions - Design & Analysis of Algorithms

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6 sample questions

Question 1.
Define a bipartite graph.
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Think about how the vertices are structured.
Question 2.
What is a perfect matching?
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Consider scenarios with distinct pairs.
3Question 3.
What is a bipartite graph?
- A graph with one set of vertices
- A graph with two distinct vertex sets
- A graph with edges only between its vertices
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Remember the characteristics of vertex sets.
4Question 4.
True or False: A perfect matching can exist in an unbalanced bipartite graph.
- True
- False
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Consider the implications of unequal sets.
Question 5.
Imagine a scenario with three courses and five teachers, each having different preferences. Model this using a bipartite graph, and determine if a perfect matching exists.
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Check each teacher’s preferences and map them accordingly.
Question 6.
Transform the following teacher-course assignments into a network flow diagram: Teacher 1 (Math, History), Teacher 2 (Biology), Teacher 3 (Economics). How would you represent this in a flow network?
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Visualize how flow connects the teachers to the courses.

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