Lecture Notes On Design And Analysis Of Algorithms

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

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

Fundamentals of Algorithms with Applications

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

NA Pages

Advanced Algorithms Lectures by Shuchi Chawla

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

195 Pages

Approximation Algorithms

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