This book "Divide and Conquer Algorithms for Multi-dimensional Problems" not only present algorithms and analysis of advanced real-life problems but also prepares you to have a deep understanding of how these algorithms were originally designed and an ability to solve some of the most insightful algorithmic problems.
This is a must read if you want to dive deeper into understanding Algorithms and its advanced applications.
Multidimensional divide and conquer is an algorithmic technique that can be used to develop several algorithms and data structures for multi-dimensional problems. It is an extension of Divide and Conquer algorithms.
The basic idea of Divide and Conquer is to divide the problem into smaller problems, solve the smaller problems and use the answers from the smaller problems to get the answer to the larger problem.
Merge Sort is a popular algorithm that applies Divide and Conquer to sort 1-dimensional data.
Extending such algorithms for Multi-dimensional data is not simple but it is an interesting approach that which nurture your thinking process and is more widely used as it reflects real-life problems.
This is important as most real-life problems are multi-dimensional like:
o A map of Earth is a 2-dimensional data
o Text is a multi-dimensional data for Clustering problems
o Augmented reality is usually 3-dimensional data
o Game graphics are at-least 3-dimensional data
o Physics consider our Universe to be 11-dimensional data
We use this paradigm to give best-known solutions to problems such as:
o Empirical Cumulative Distribution Functions problem (ECDF)
o Maxima problem
o Range searching problem
o Closest pair problem
o All nearest neighbor problems
For all problems, we have demonstrated 1-dimension problem, 2-dimension problem, 3-dimension problem, k-dimension problem (all with time complexity analysis) and real-life applications.
We, also, presented open question in this domain which you can think about and potentially, develop a solution.
This book has been carefully prepared and reviewed by Algorithmic researchers at OpenGenus and Tokyo Institute of Technology. We would like to thank Aditya Chatterjee and Benjamin QoChuk for their expertise in this domain.
Read this book now and change the way you think about algorithms. This is a must read for everyone who wants to truly understand Algorithms and apply it to solve advanced problems.