Fundamentals of Algorithms

CS502-Spring 2011 

Assignment #5

Deadline

 Your assignment must be uploaded/submitted at or before 8^th JULY 2011

Uploading instructions

 Please view the assignment submission process document provided to you by the Virtual University to upload the assignment.

Rules for Marking

 It should be clear that your assignment will not get any credit if:

• The assignment is submitted after due date.
• The submitted assignment does not compile or run.
• The assignment is copied.

Objectives

This assignment will help you to understand the concepts of Knapsack Problem and Chain matrix Multiplication which results in efficient calculation time wise.

Guidelines

1. 1. In order to attempt this assignment you should have full command on Lecture # 39to Lecture # 45
2. 2. In order to solve this assignment you have strong concepts about following topics

• Polynomial Time Algorithms
• Non deterministic Polynomial time Algorithims

Recommended book for solving assignment

Cormen, Leiserson, Rivest, and Stein (CLRS) 2001, Introduction to Algorithms, (2nd ed.) McGraw  Hill.

Estimated Time    3  hours

You can make justified search for the topic in One hour and 1.5 hour to understand the whole themes you are asked and 0.5 hour to organize and type whole material.

What to submit

You are bound to submit word file only in the given format and given HEADLINES below. Negative marking will be done in case of violating the format provided to you. 

Question# 1 (9)

You are bound to answer the following queries relating to Polynomial time/space algorithms:

Formal Definition 1.5

How the given problem is identified the Problem is in P class

[You are only bound to give some hints/theorems no detail proofs]   4

Are these problems Feasible to Solve in available memory and time                       2

[Why or why not give constraints if any]

Examples                1.5

[General type examples are preferable]

Question# 2 (9)

You are bound to answer the following queries relating to Non Deterministic Polynomial time/space algorithms:

Formal Definition 1.5

How the given problem is identified the Problem is in NP class 4

[You are only bound to give some hints/theorems no detail proofs, some more hints relating to NP classes are  preferable]

Are these problems Feasible to Solve in available memory and time                       2

[Why or why not give constraints if any]

Examples                1.5

[General type examples are preferable; Classes of NP can be given with single line explanation]

Q 3   Conclusions 2

[Here you have to write two to three sentences relating to final comments on P and NP problems]