These ecture notes give a comprehensive introduction to the basic techniques in the design and analysis of algorithms. It covers major methodologies, including greedy methods, which build up solutions piece by piece; dynamic programming (DP), which breaks down problems into simpler subproblems, solves them, and memorizes their solutions; and backtracking, which incrementally generates candidates for solutions and discards those that cannot satisfy criteria. It also discusses the method of Branch and Bound, where all branches on a solution space are systematically explored until the best possible solution is obtained. These methods are crucial in the design of nice algorithms with a view to efficiency, and they form the basis of complex computational problems that require solutions.
Author(s): Annamalai University
96Pages
This PDF deals with some advanced topics in the design of algorithms, focusing on Dynamic Programming. The application domains of DP are discussed and cover classic problems, including Matrix Chain Multiplication, that is, finding an optimal order to multiply many matrices, and Rod Cutting, which is just a typical 4-inch rod problem. Its notes include insights into the steps of DP, its recursive tree structures, and problem-solving through the bottom-up approach. The wide de-balcony of these topics helps the reader understand how DP can be applied to a variety of optimization problems and demonstrates both theoretical and practical aspects of algorithm design.
Author(s): BMS College of Engineering
152Pages
These all are very extensive notes on fairly advanced topics in algorithms—both theoretical and practical. Here we deal with discrete algorithms for minimum spanning trees, arborescences (directed spanning trees), dynamic algorithms for problems in graph connectivity, and the shortest path. Other topics discussed in the paper are the combinatorial, algebraic algorithms for graph matching techniques and their corresponding challenges developed within high-dimensional spaces via the technique of dimension reduction and streaming algorithms. Other topics but not triangulated within include the approximate max-flows, online learning, and interior-point methods. The notes thus present a framework in its totality for learning and analyzing super advanced algorithms and thus become a good source to glean insights for an ocean of problems in computer science.
Author(s): Anupam Gupta
309Pages
Dr. Subasish Mohapatra's Lecture Notes on Design and Analysis of Algorithms, published on August 2, 2022, is a big 125-pages book to cover many of the algorithmic core ideas. It contains the core ideas such as growth of functions and recurrences, with great detail on the solving of these via substitution, recursion trees, and the Master Method. Discussion of detailed Divide and Conquer algorithms, along with worst-case running times for problems such as merge sort, quick sort, and binary search, is also covered. Heaps, heap sort, priority queues, and sorting lower bounds are discussed. Detailed discussions of dynamic programming techniques cover the matrix chain multiplication problem, longest common subsequence problem, and general strategies. Discussions of robust algorithms based on dynamic programming that cover applications such as the activity selection problem, fractional knapsack problem, and Huffman coding. It also comprises graph algorithms, for instance: BFS, DFS, minimum spanning trees, Kruskal's, and Prim's.
Author(s): Dr. Subasish Mohapatra
125Pages
Lecture Notes on Design and Analysis of Algorithms by Mr. S.K. Sathua, Dr. M.R. Kabat, and Dr. R. Mohanty, published November 14, 2020, is an 80-page document that provides a vital summary of some of the significant notions of algorithms. It first of all provides the basics of the growth of functions and recurrences, while techniques for the solution of these recurrences include substitution and recursion trees. These notes introduce the Master Method for analyzing divide and conquer algorithms and provide worst-case analysis of merge sort, quick sort, and binary search. Other topics it covers are heaps, heap sort, priority queues, and sorting lower bounds, thus proving very valuable for comprehending core principles in algorithm analysis and design.
Author(s): Mr. S.K. Sathua, Dr. M.R. Kabat and Dr. R. Mohanty
80Pages
Design and Analysis of Algorithms is a book by Herbert Edelsbrunner that gives a detailed description of the basic principles and techniques of algorithms. The book offers basic data structures and some graph algorithms, making it one of the best platforms to understand how to design and analyze algorithms. It emphasizes the developers developing a good and efficient algorithm, followed by the analysis of complexity. It contains basic data structures such as trees, graphs, and several strategies of algorithmic problem-solving. Edelsbrunner's approach in the text marries theoretical insights with the practical details that are absolutely necessary to implement his algorithms. So, his book will be of great use to students, researchers, and practitioners concerned with algorithms in computer science. The book will help the readers to incite strong skills in algorithmic techniques and their applications and create an overview necessary for a deeper understanding of computational efficiency and problem solving.
Author(s): Herbert Edelsbrunner
95Pages
Michael T. Goodrich's Fundamentals of Algorithms with Applications gives good coverage to algorithmic principles and their application. It covers growth functions, basic data structures, sorting, selection, dynamic programming, graph algorithms-the principles of algorithm design. Advanced topics such as NP-completeness, approximation algorithms, and randomized algorithms are also explored. Goodrich's book is well-recognized for its lucid explanations of the exercises on these complex topics to make them understandable and lively. Theoretically sound, with practical applications, this book suits both students and professionals in developing problem-solving skills and computational understanding.
Author(s): Michael T. Goodrich
NAPages
Advanced Algorithms" by Prof. Michel Goemans is an advanced-level text focused on sophisticated algorithmic methods for doctoral students and researchers. Advanced subjects like Fibonacci heaps, network flows, and dynamic trees are explained in detail, together with linear programming-the Goldberg-Tarjan min-cost circulation algorithm, approximation algorithms, max-cut problems, and conic programming. Goemans explains such advanced concepts in great detail, merging theory and practice. This text will be useful for anyone interested in deeply understanding modern algorithms and how they may be implemented and includes a conceptual framework for rigorous solutions to complex computational problems.
Author(s): Prof. Michel Goemans
NAPages
The book Data Structures and Algorithms by Sugih Jamin covers all the basic concepts of Computer Science in a very balanced way. It involves topics such as linked lists, stacks, and queues to more advanced topics such as binary search trees, heaps, and balanced search trees. Jama's text emphasizes an implementation perspective and algorithmic patterns, which will facilitate a more effective way of understanding and applying the concepts presented. This book will be very useful for the students and professionals who want to establish a sound foundation in data structures and algorithms by providing a solid theoretical background supported by practical examples that explain how problems are solved.
Author(s): Sugih Jamin
NAPages
Prof. Nancy Lynch's Distributed Algorithms Lecture Notes has a great amount of detail concerning algorithms designed for distributed systems within which important aspects are that of multiple processors executing without centralized control. This paper investigates the model assumptions and organization strategies tasked with the two basic timing models. It also looks at synchronous, asynchronous, and partially synchronous models and synchronous networks. They discuss various models, thus enable the researchers to understand what one is actually up against and what strategies one can use in order to design algorithms working effectively in distributed environments. Hence, Lynch's notes are a must-have for any researcher who aims to know how to manage communication and coordination in distributed systems. Therefore, ideal for use by students and professionals dealing with distributed computing and networked systems.
Author(s): Prof. Nancy Lynch
NAPages
Advanced Algorithms Lectures by Shuchi Chawla give an insight into advanced techniques in the design and analysis of algorithms. The lectures cover topics such as greedy algorithms, dynamic programming, and network flow applications. Advanced topics, including randomized algorithms and Karger's min-cut algorithm, NP-completeness, together with linear programming, primal-dual algorithms, and semi-definite programming, are discussed. Chawla also deals with models like Probably Approximately Correct (PAC) and boosting within this framework. This set of lectures comprehensively covers advanced algorithmic methodologies along with their applications and constitutes an excellent resource for students and researchers interested in advanced classes of algorithmic techniques and their applications to pressing real-world problems.
Author(s): Shuchi Chawla
195Pages
The lecture notes on Approximation Algorithms by Shuchi Chawla focus on techniques of designing algorithms that produce near-optimal solutions to complex optimization problems for which finding an exact solution is computationally infeasible. These lecture notes cover general underlying techniques of approximation algorithms, comprising basic building blocks and the foundation needed to deal with problems which are difficult to solve exactly due to computational complexity. These notes by Chawla provide an outline of various methods for approaching different optimization problems and ways of solving them when exact algorithms are not practical. Further, this resource is likely to be extremely helpful with respect to devising and applying approximation algorithms returning good solutions within a reasonable amount of time; hence, this is a must for scholars and practitioners faced with hard optimization problems.
Author(s): Shuchi Chawla
NAPages
