11.1.5. Efficiency of Reductions

Try these first

1. 1.

   Define what a reduction in algorithm design means.

   Hint

   Think about simplification and reformation of problems.

2. 2.

   What distinguishes a bipartite graph?

   Hint

   Consider the division of entities in a matching situation.

3. 3.

   What is the main purpose of a reduction in the context of algorithms?

   • To simplify a problem
   • To use algorithms of another problem
   • Both A and B

   Hint

   Consider the roles reductions play in problem-solving.

4. 4.

   True or False: A bipartite graph contains edges only within the same set of vertices.

   • True
   • False

   Hint

   Visualize the graph and its structure to recall the definition.

5. 5.

   Suppose you have 5 teachers and 4 courses. Write a brief outline on how you would set up a bipartite graph for this scenario, drawing from the matching criteria discussed.

   Hint

   Think about the limits of matching and how to illustrate preferences graphically.

6. 6.

   Design a hypothetical scenario in which the reduction from a bipartite matching to a network flow helps solve a more complex problem in allocation.

   Hint

   Envision resource maximization in terms of nodes and flows.