Dr. Madani Naidjate
Dr. Madani Naidjate Shares His Passion For Algorithmic Solutions To Practical Problems
Madani Naidjate
Lecturer, Computer Science
Professor of Mathematics and Director, Berenson Center for Mathematics at Dean College
PhD, Boston University; MS, Boston University; BS, Polytechnic Institute of Algiers, Algeria
What is your area of expertise?
I specialize in applied mathematics, telecommunications, and computing.
Please tell us about your work. Can you share any current research or recent publications?
To begin my career, I worked in IT and consulting for a financial firm for about twelve years. About twenty years ago, I switched to academia on a full-time basis. I have always been interested in teaching and sharing knowledge with others. It turned into a passion of mine.
The strong interaction that theoretical computer science offers between abstract mathematics and the practical world has been the center of my focus. My research interests include algebraic, probabilistic, and geometric tools to solve combinatorial and algorithmic problems.
I’ll provide you with some examples of my research.
A serious problem in a digital data communication system is the occurrence of errors in the data transmitted over a noisy channel. A major concern to the communication engineer is controlling these errors such that reliable transmission of data can be obtained. One of the problems that my research tackled was the minimum distance decoding (MDD) for a general linear code, which remains a difficult computational problem. Even though the problem was shown to be NP-hard, the Identity-Guards algorithm was proposed. It makes use of a special subset of codewords called Identity-Guards. I was able to estimate the number of Identity-Guards using geometric and probabilistic approaches.
The geometric approach yields a very rough bound while the probabilistic method gives a more general expected value expression for any random group code. Furthermore, I generalized the algorithm for any block code that possesses a group structure, not necessarily Abelian, defined in a metric space, with a left-invariant metric d. The theory has been generalized to both continuous spaces (decoding spherical codes), and strictly discrete spaces. I would like to explore the generalization of the IGA to Arithmetic codes and Permutation codes, namely Matthew groups—a little technical, I know!
Another problem that I worked on is the “S-surjective Exhaustive Test Patterns Generation for Combinational and Sequential Circuits”. The research here focused on presenting an approach to the problem of functional testing of combinational and sequential devices. The tremendous modern development of very large-scale integration (VLSI) technology produced a difficult new challenge—the problem of determining whether or not a digital circuit operates correctly. Micro-miniaturization of components and the increase of packing yield some inevitable faults. Rates of faulty chips may reach up to 20%, and tests became more and more costly. A partial solution to the problem is exhaustive pattern testing. My contribution to this problem was the development of probabilistic and deterministic algorithms using linear and constant weight codes to minimize the number of test patterns.
How does the subject you work in apply in practice? What is its application?
The minimum distance decoding problem is part of the study of coding theory. Codes are used for data compression, cryptography, error detection and correction, data transmission, data storage, and data compression. Because of this, exhaustive test pattern generation has direct applications in computer hardware testing.
What courses do you teach at BU MET?
Over the years, I have taught a wide variety of courses at BU MET. Most often, I teach Discrete Mathematics (MET CS 248), Computers and Their Applications (MET CS 101), Analysis of Algorithms (MET CS 566), and Computer Language Theory (MET CS 662).
Please highlight a particular project within a course that most interests your students. What “real-life” exercises do you bring to class?
One of the most interesting exercises, for both the students and myself, comes in my Analysis of Algorithms class. The students pick a topic of their choice, that I then approve, before they present to the rest of the class. Topics usually pertain to their respective workplaces, and their presentations are a unique experience. The exchange of comments and fresh ideas between all participants makes the class vibrant and interesting. Having students exposed to more than a dozen-and-a-half different sorting algorithm, side by side, and discussing the different features of each of them is definitely one of the highlights of the course.
What do you consider the unique value you bring to the classroom?
I bring rigor to the class, as well as a commitment to helping students understand and appreciate logic and mathematics and the relevance of theory in computer science. Through my lessons, I expose students to the wide applications of theory.