4. cs8451 daa anna univ question bank unit 4

1. 1
DEPARTMENT OF INFORMATION TECHNOLOGY
Subject Code : CS8451 Subject Name : Design & Analysis ofAlgorithms
Class/ Sem : II IT / III Sem Subject In – Charge : Dr. P. Subathra, Prof./IT
QUESTION BANK
UNIT IV
ITERATIVE IMPROVEMENT 9 The Simplex Method - The Maximum-Flow Problem –
Maximum Matching in Bipartite Graphs, Stable marriage Problem.
Principle of duality
Q. No Question
Marks
Knowled
geLevel
Number
of
Times
inAU
PART - A
ITERATIVE IMPROVEMENT: The Simplex Method
1. Define the iterative improvement technique. (R 13 NOV/ DEC 2016)
2. Describe its iterative improvement technique. (R13 NOV/ DEC 2018) Define
multistage graphs. Give an example. (R13 NOV/ DEC 2018)
ITERATIVE IMPROVEMENT: The Maximum-Flow Problem
3. Define flow ‘cut’. (R 13 APR/MAY 2015)
4. Define Network Flow and Cut. (R 13 NOV/ DEC 2015)
5. Define the capacity constrain in the context of maximum flow problem. (R 17
APR/MAY2019)
6. Define flow 'cut'. (R13 APR/MAY2019)
7. How is transportation network represented? (R13 APR/MAY2018)
ITERATIVE IMPROVEMENT: Maximum Matching in Bipartite Graphs
8. What do you mean by “perfect matching” in bipartite graph? (R 13 APR/MAY
2015)
9. What is maximum cardinality matching? (R 13 NOV/ DEC 2016)

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10. What do you mean by “perfect matching” in bipartite graphs? (R 13 APR/MAY
2017)
11. State: Planar colouring graph problem. (R 13 APR/MAY 2017)
12. What are Bipartite Graphs? (R 13 NOV/ DEC 2017)
13. What do you mean by 'perfect matching' in bipartite graphs? (R13 APR/MAY
2019)
14. What is meant by maximum cardinality matching? (R13 APR/MAY2018)
ITERATIVE IMPROVEMENT: Stable marriage Problem.
Q. No Question
Marks
Knowled
geLevel
Number
of
Times
inAU
PART - B
ITERATIVE IMPROVEMENT: The Simplex Method
1. List the steps in Simplex Method and give the efficiency of the same. (R 13
NOV/ DEC 2017) (13)
2. Summarize the steps of the Simplex Method. (R 13 NOV/ DEC 2016) (8)
3. Describe in detail the simplex algorithm methods. (R 13 APR/MAY 2017) (13)
4. Summarize the simplex method. (R 13 MAY/JUN 2016) (8)
5. Summarize the steps of the simplex method. (R13 APR/MAY2019) (8)
6. Illustrate the steps of the simplex methods with an example. (R13 NOV/ DEC
2018) (13)
7. Maximize p=2x+3y+z; subject to: x+y+z<=40; 2x+y-z>=10; -y+z>=10;
x>=0;y>=0;z>=0. (R 13 APR/MAY 2015) (8)
8. Maximize 3a+2b+c subjected to: (R 13 NOV/ DEC 2015) 2a+b+c<=3;
a+b+c<=4; 3a+3b+6c<=6; a,b,c>=0.
9. Write the procedure to initialize Simplex which determines if a linear program is
feasible or not? (R 13 NOV/ DEC 2015) (14)

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10. Solve the following set of equations using Simplex algorithm: (R 17 APR/MAY
2019) (13)
Maximize : 18x1+12.5x2
Subject to: x1+x2 <=20
x1<=12
x1,x2>=0.
ITERATIVE IMPROVEMENT: The Maximum-Flow Problem
11. How do you compute maximum flow for the following graph using Ford-
Fulkerson method? (R 13 APR/MAY 2015) (10)
12. State and prove Max-Flow Min-Cut Theorem. (R 13 NOV/ DEC 2016) (8)
13. Explain Max-Flow Problem. (R 13 NOV/ DEC 2015) (4)
14. State and prove Max-Flow Min Cut Theorem. (R13 APR/MAY2019) (7 )
15. State and prove Max-Flow Min-Cut Theorem. (R 13 MAY/JUN 2016) (8)
16. Apply the shortest-augmenting path algorithm to the network shown below. (R
13 MAY/JUN 2016) (16)
17. Determine the Max-Flow in the following graph: (R 17 APR/MAY2019) (13)
ITERATIVE IMPROVEMENT: Maximum Matching in Bipartite Graphs
18. Write down the optimality condition and algorithmic implementation for finding
M-augmenting paths in bipartite graphs. (R 13 APR/MAY 2015) (8)

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19. Illustrate the working of the maximum matching algorithm on the following
weighted tree. (R 13 NOV/ DEC 2015) (12)
ITERATIVE IMPROVEMENT: Stable marriage Problem.
20. What is stable marriage problem? Give the algorithm and analyze it. (R 13 NOV/
DEC 2017) (13)
21. Briefly describe on the Stable Marriage Problem. (R 13 APR/MAY 2015) (6)
22. Explain briefly about Stable Marriage Algorithm. (R 13 NOV/ DEC 2016) (10)
23. Determine the time-efficiency class of the stable marriage algorithm. (R 13 NOV/
DEC 2016) (6)
24. Write the stable marriage algorithm and trace it with an instance. Analyze its
running time complexity. (R13 NOV/ DEC 2018) (13)
25. Explain briefly about Stable marriage algorithm. (R13 APR/MAY2019) (7)
26. Give the summary of the simplex method. (R13 APR/MAY2018) (13)
27. Determine the time-efficiency class of the stable marriage algorithm. (R13
APR/MAY2019) (8)
28. Prove that the stable marriage algorithm terminates after no more than n2
iterations with a stable marriage output. (R13 APR/MAY2018) (13)
Q. No Question
Marks
Knowled
geLevel
Number
of
Times
inAU
PART - C
ITERATIVE IMPROVEMENT: The Simplex Method

5. 5
1. Use Simplex to solve the farmers problem given below:
A farmer has a 320 acre on which he plants two crops: rice and wheat. For each
acre of rice planted, his expenses are 50 and for each acre of wheat planted, his
expenses are 100. Each acre of rice requires 100 quintals of storage and yields a
profit of 60; each acre of wheat requires 40 quintals of storage and yields a profit
of 90. If the total amount of storage space available is 19,200 quintals and the
farmer has only “20,000” on hand, how many acres of each crop should he plant
in order to maximize his profit? What will his profit be if he follows this
strategy? (R 13 NOV/ DEC 2015) (12)
Staff In – Charge Subject Matter Expert HoD/IT