Practice Perfect Match and Network Flows - 11.1.3 | 11. Reductions | Design & Analysis of Algorithms - Vol 3
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11.1.3 - Perfect Match and Network Flows

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a bipartite graph.

💡 Hint: Think about how vertices are organized.

Question 2

Easy

What does a perfect match in a bipartite graph mean?

💡 Hint: Consider what 'one-to-one' pairing means.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is a bipartite graph?

  • A graph with only one set of vertices
  • A graph where edges connect two distinct sets of vertices
  • A graph with cycles only

💡 Hint: Think about how vertices are paired.

Question 2

True or False: A perfect matching requires that at least one vertex in the bipartite graph be left unmatched.

  • True
  • False

💡 Hint: Relate this to the definition of 'perfect'.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider a school with 5 teachers: T1, T2, T3, T4, T5 and 4 courses: C1, C2, C3, C4. The preferences are as follows: T1 (C1, C2), T2 (C2, C3), T3 (C3), T4 (C1), T5 (C2, C4). Determine if a perfect matching exists and justify your answer.

💡 Hint: Remember to evaluate all teachers' potential matches before concluding.

Question 2

A university has to assign courses among 6 professors and 5 classes, where classes have specific capacity limits and professors have their preferences. Develop a flow network and find a maximum flow configuration that indicates potential assignments.

💡 Hint: Keep track of the flow capacities while ensuring no professor is overloaded beyond their willing assignments.

Challenge and get performance evaluation