Memory Efficient Algorithm

1. A Presentation on Memory Effcient Algorithms
April 2019 CSE6408
Student ID:0419052090
Bangladesh University of Engineering and Technology
July 2, 2019
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2. Low Memory Algorithm
Motivation
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3. Low Memory Algorithm
Motivation
In-place Model
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4. Low Memory Algorithm
Motivation
In-place Model
Read-Only Model
Time Interval Problem
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5. Low Memory Algorithm
Motivation
In-place Model
Read-Only Model
Time Interval Problem
Snake/Snail Problem
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6. Low Memory Algorithm
Motivation
In-place Model
Read-Only Model
Time Interval Problem
Snake/Snail Problem
Cycle Counting Problem
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7. Objective:
Objective of memory efficient algorithm is to reduce working storeage
requirement in the expense of limited inefficiency in the running time.
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8. In-place-Model:
Input data can be changed during the execution and after execution
each object is in the input array
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9. Read-Only-Model:
Input data structure is read only memory that is input data structure
remains unchanged after execution.Here we solve all the problem
using Read-only-Model.
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10. Time Interval Problem
Problem Definition:
Suppose you are working for a company. You are now looking at a
list of monthly profit and loss and wonder when the company was
best. To measure the company’s commercial activity, you can define
the total amount of profit for consecutive months.
month 1 2 3 4 5 6 7 8 9 10 11 12
profit 4 -3 5 -7 9 -2 5 -7 9 -2 -5 6
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11. Algorithm 1
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13. Algorithm 1
Time complexity O(n2)
Space complexity O(n2)
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15. Algorithm 2
Time complexity O(n2)
Space complexity O(n)
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16. Algorithm 3
month 1 2 3 4 5 6 7 8 9 10 11 12
profit 4 -3 5 -7 9 -2 5 -7 9 -2 -5 6
Sum 4 1 6 -1 8 6 11 4 13 11 6 12
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18. Algorithm 3
Time complexity O(n)
Space complexity O(n)
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20. Lemma
Given a list of profit and loss for n months in a read-only array,
Algorithm 4 finds the best time interval in O(n) time without using
an extra array.
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21. Snake or Snail: Detection of a Cycle Problem
Problem Definition:
Suppose we have a linked list with single pointers. Given a pointer to
the head of such a linked-list, we want to determine whether it
contains a cycle or not.
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22. Snake
When we traverse the list one after another,if NULL is found at any
point the it will be considered as ”Snake”.
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23. Snail
If the exist a cycle in the list then it will be considered as ”Snail”.
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25. Algorithm 1
Time complexity O(n2)
Space complexity O(n)
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27. Algorithm 2
Time complexity O(n)
Space complexity O(n)
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28. Algorithm 3:The Tortoise and Hare Algorithm
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30. Algorithm 3
Time complexity O(n)
Space complexity O(1)
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31. Lemma
Algorithm T and H correctly determine snake/snail distinction of a
given list containing n list elements in O(n) time using only O(1)
working space.
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32. Cycle Counting Problem
Problem Definition:
Given a 2-regular graph G by a sequence of n pairs on integers
between 1 and n on a read-only array, give an efficient algorithm
which counts the number of cycles in G using only constant work
space.
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33. 2-Regular Graph:
A 2-Regular Graph is a regular graph where number of degree of each
vertex is 2 i.e,each vertex has 2 edge.
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35. Algorithm 1
Time complexity O(n)
Space complexity O(n)
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37. Algorithm 2
Time complexity O(n2)
Space complexity O(1)
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39. Algorithm 3
Time complexity O(nlogn)
Space complexity O(1)
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40. Thank You!
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