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Advanced Algorithms · End Term · 24 Dec 2023 · September 2023 term · Set FDB1

Question 10: Consider the following bipartite graph: the set A is com…

Question 10

+2 marksOne correct option

You have been given a R × C chessboard, with a list of squares cut out. This problem will involve placing rooks on a chessboard, so that they cannot attack each other. For a rook to attack a target piece, it must share the same row or column as the target.
Find the maximum number of rooks that can be placed on the chessboard, such that no pair of rooks can attack each other.
Rooks cannot be placed on cut out squares. The cut out squares do not affect where the rooks can attack.
Based on the above data, answer the given subquestions.

Consider the following bipartite graph: the set A is composed of elements corresponding to every row of the board, while set B consists of the columns. For each row add edges to every column if the corresponding square is not cut out of the board. What does the answer correspond to in this graph?

  1. A

    the maximum vertex degree

  2. B

    the number of edges in a minimum spanning forest

  3. C

    the size of a maximum matching

  4. D

    none of these

Show answer

Correct answer

  • C

    the size of a maximum matching

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Question 10 of 24 in the IIT Madras BS Advanced Algorithms (Advanced Algorithms) End Term paper sat on 24 Dec 2023, in the September 2023 term (IIT M DEGREE FN EXAM FDB1 24 Dec 2023). It carries 2 marks.

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