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
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
NA Pages
