Introduction to Design & Analysis of Algorithms -In Simple Way

1997

Algorithms and programming : problems and solutions I Alexander Shen. p. cm. Includes bibliographical references and index.

Maple Transactions

Teaching analysis of algorithms to students in Computer Science degrees, using the approach popularized by Knuth in his series of books ``The Art of Computer Programming" and later by Sedgewick and Flajolet in the book ``An Introduction to the Analysis of Algorithms", is not a simple task since, in general, these students are more interested in the implementation of an algorithm than in the corresponding theoretical aspects. This approach concentrates on precisely characterizing the performance of algorithms by determining their best, worst and average case performance using a methodology based on symbolic tools such as recurrence relations and generating functions.The most difficult aspect is to understand the average case since this corresponds to studying the algorithm as its possible inputs vary: this represents the most important goal since generally students have no difficulty in understanding the best and worst cases, corresponding to particular input configurations...

Nonconvex optimization and its applications, 2002

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.-Albert Einstein In theory there is no difference between theory and practice. In practice there is.-Yogi Berra T he algorithm and the program. The abstract and the physical. If you want to understand the fundamental and universal properties of a computational process, study the abstract algorithm and prove a theorem about it. If you want to know how the process really works, implement the algorithm as a program and measure the running time (or another quantity of interest). This distinction between the abstract model and the physical artifact exists in the study of computational processes just as in every other area of mathematical modeling. But algorithmic problems have some unusual features. For example, we usually build models to serve as handy representations of natural phenomena that cannot be observed or manipulated directly. But programs and computers are completely accessible to the researcher and are far more manipulable than, say, weather patterns. They are also much easier to understand: hypothetically, one could obtain complete information about the behavior of a program by consulting technical documents and code. And finally, algorithms are usually invented before programs are implemented, not the other way around. This article surveys problems and opportunities that lie in the interface between theory and practice in a relatively new research area that has been called experimental algorithmics, experimental analysis of algorithms, or algorithm engineering.

Lecture Notes in Computer Science, 2006

have taken a course in continuous algorithms (numerical analysis) in the junior year, and in discrete algorithms in the senior year. This book has grown out of the senior course as I have been teaching it recently. It has also been tried out on a large class of computer science and mathematics majors, including seniors and graduate students, with good results. Selection by the instructor of topics of interest will be very important, because normally I've found that I can't cover anywhere near all of this material in a semester. A reasonable choice for a first try might be to begin with Chapter 2 (recursive algorithms) which contains lots of motivation. Then, as new ideas are needed in Chapter 2, one might delve into the appropriate sections of Chapter 1 to get the concepts and techniques well in hand. After Chapter 2, Chapter 4, on number theory, discusses material that is extremely attractive, and surprisingly pure and applicable at the same time. Chapter 5 would be next, since the foundations would then all be in place. Finally, material from Chapter 3, which is rather independent of the rest of the book, but is strongly connected to combinatorial algorithms in general, might be studied as time permits. Throughout the book there are opportunities to ask students to write programs and get them running. These are not mentioned explicitly, with a few exceptions, but will be obvious when encountered. Students should all have the experience of writing, debugging, and using a program that is nontrivially recursive, for example. The concept of recursion is subtle and powerful, and is helped a lot by hands-on practice. Any of the algorithms of Chapter 2 would be suitable for this purpose. The recursive graph algorithms are particularly recommended since they are usually quite foreign to students' previous experience and therefore have great learning value. In addition to the exercises that appear in this book, then, student assignments might consist of writing occasional programs, as well as delivering reports in class on assigned readings. The latter might be found among the references cited in the bibliographies in each chapter. I am indebted first of all to the students on whom I worked out these ideas, and second to a number of colleagues for their helpful advice and friendly criticism. Among the latter I will mention Richard Brualdi, Daniel Kleitman, Albert Nijenhuis, Robert Tarjan and Alan Tucker. For the no-doubt-numerous shortcomings that remain, I accept full responsibility. This book was typeset in T E X. To the extent that it's a delight to look at, thank T E X. For the deficiencies in its appearance, thank my limitations as a typesetter. It was, however, a pleasure for me to have had the chance to typeset my own book. My thanks to the Computer Science department of the University of Pennsylvania, and particularly to Aravind Joshi, for generously allowing me the use of T E X facilities.