Introduction to Algorithms Lecture Notes

Advanced Algorithms by BMS College of Engineering

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

152 Pages

Advanced Algorithms by Anupam Gupta

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

309 Pages

Lecture Notes On Design And Analysis Of Algorithms

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

125 Pages

Design And Analysis Of Algorithms by Herbert Edelsbrunner

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

95 Pages

Data Structures And Algorithms by Sugih Jamin

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

NA Pages

Distributed Algorithms Lecture Notes

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

NA Pages