A Guide to Design and Analysis of Algorithms

126 Pages·2023·12.535 MB·English

by  Soubhik Chakraborty, Prashant Pranav, Naghma Khatoon, Sandip Dutta

Computer Science, Technology
and Applications
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Soubhik Chakraborty, Prashant Pranav,
Naghma Khatoon and Sandip Dutta
A Guide to Design
and Analysis of Algorithms
Copyright © 2023 by Nova Science Publishers, Inc.
DOI: https://doi.org/10.52305/HVZD7283
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Contents

Preface .......................................................................................... vii
Chapter 1 Introduction to the Design of Algorithms ........................1
Chapter 2 Divide and Conquer ........................................................11
Chapter 3 Greedy Algorithms ..........................................................19
Chapter 4 Dynamic Programming ...................................................27
Chapter 5 Backtracking ....................................................................45
Chapter 6 Branch and Bound ...........................................................51
Chapter 7 Introduction to the Analysis of Algorithms ...................67
Chapter 8 Randomized Algorithms .................................................81
Chapter 9 Master Theorem ..............................................................91
Chapter 10 A Note on Empirical Complexity Analysis ....................97
References ......................................................................................... 109
About the Authors .................................................................................... 111
Index ......................................................................................... 113

Preface

As there can be more than one algorithm for the same problem, designing and
analysing an algorithm becomes important in order to make it efficient and
robust as far as possible. This book would serve as a guide to design and
analysis of computer algorithms.
Chapter 1 gives an overview of different algorithm design techniques and
the various applications of the discussed techniques. Brute force approach,
divide and conquer design approach, greedy algorithms, dynamic
programming, branch and bound technique, backtracking and randomized
algorithms are discussed in this chapter. Chapter 2 discusses the divide and
conquer strategy and some of the algorithms that employs this technique such
as recurrence relation, binary search and merge sort. Chapter 3 gives an
insight into the greedy algorithms and some problems that can be solved using
the greedy approach like the job sequencing problem with deadline and the
Dijkstra algorithm. Chapter 4 discusses in depth the dynamic programming
approach. Problems such as the stagecoach problem, optimal binary search
tree, 0/1 knapsack problem and the subset sum problem are discussed in this
chapter. Chapter 5 deals with the backtracking approach with a solution to the
N – Queens problem using this approach. Chapter 6 throws some light on the
branch and bound technique. Solution to three famous problems viz.
assignment problem, 0/1 knapsack problem and travelling salesman problem
are discussed using the branch and bound technique.
Chapter 7 introduces the second part of the book – the analysis of
algorithms. Two different approaches to the analysis of algorithm viz. the
asymptotic analysis and the empirical analysis are discussed in the chapter.
Chapter 8 discusses randomized algorithms with an empirical analysis
touch. Randomized quick sort and randomized binary search are discussed and
analysed empirically. Chapter 9 deals with Master Theorem. Many problems
that can be solved using Master Theorem are dealt with in this chapter. Chapter
10 gives a note on the empirical complexity analysis of algorithms. Empirical
viii Soubhik Chakraborty, Prashant Pranav, Naghma Khatoon et al.
complexity of four prominent sorting algorithms – merge sort, quick sort,
bubble sort and selection sort have been discussed in depth in this chapter.
The authors thank Nova Science Publishers for accepting the challenge to
publish this work in a book form.

Soubhik Chakraborty
Prashant Pranav
Naghma Khatoon
Sandip Dutta