mathematics

Narendra Karmarkar

Narendra Karmarkar is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Narendra Karmarkar rather than just read about it. In short: Narendra Krishna Karmarkar (born 1956) is an Indian mathematician. He developed Karmarkar's algorithm.

Key takeaways

Narendra Karmarkar belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Narendra Karmarkar to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Narendra Karmarkar from memory before moving on to harder problems.

Reference excerpt

Narendra Krishna Karmarkar (born 1956) is an Indian mathematician. He developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher. He invented one of the first provably polynomial time algorithms for linear programming, which is generally referred to as an interior point method. The algorithm is a cornerstone in the field of linear programming. He published his famous result in 1984 while he was working for Bell Laboratories in New Jersey.

Biography Karmarkar received his B.Tech. in electrical engineering from IIT Bombay in 1978, M.S. from the California Institute of Technology in 1979, and Ph.D. in Computer Science from the University of California, Berkeley in 1983 under the supervision of Richard M. Karp. Karmarkar was a post-doctoral research fellow at IBM research (1983), Member of Technical Staff and fellow at Mathematical Sciences Research Center, AT&T Bell Laboratories (1983–1998), professor of mathematics at M.I.T. (1991), at Institute for Advanced study, Princeton (1996), and Homi Bhabha Chair Professor at the Tata Institute of Fundamental Research in Mumbai from 1998 to 2005. He was the scientific advisor to the chairman of the TATA group (2006–2007). During this time, he was funded by Ratan Tata to scale-up the supercomputer he had designed and prototyped at TIFR. The scaled-up model ranked ahead of supercomputer in Japan at that time and achieved the best ranking India ever achieved in supercomputing. He was the founding director of Computational Research labs in Pune, where the scaling-up work was performed. He continues to work on his new architecture for supercomputing.

Work

Karmarkar's algorithm

Karmarkar's algorithm solves linear programming problems in polynomial time. These problems are represented by a number of linear constraints involving a number of variables. The previous method of solving these problems consisted of considering the problem as a high-dimensional solid with vertices, where the solution was approached by traversing from vertex to vertex. Karmarkar's novel method approaches the solution by cutting through the above solid in its traversal. Consequently, complex optimization problems are solved much faster using the Karmarkar's algorithm. A practical example of this efficiency is the solution to a complex problem in communications network optimization, where the solution time was reduced from weeks to days. His algorithm thus enables faster business and policy decisions. Karmarkar's algorithm has stimulated the development of several interior-point methods, some of which are used in current implementations of linear-program solvers.

Galois geometry After working on the interior-point method, Karmarkar worked on a new architecture for supercomputing, based on concepts from finite geometry, especially projective geometry over finite fields.

Awards The Association for Computing Machinery awarded him the prestigious Paris Kanellakis Award in 2000 for his work on polynomial-time interior-point methods for linear programming for "specific theoretical accomplishments that have had a significant and demonstrable effect on the practice of computing". Srinivasa Ramanujan Birth Centenary Award for 1999, presented by the Prime Minister of India. Distinguished Alumnus Award, Indian Institute of Technology, Bombay, 1996. Distinguished Alumnus Award, Computer Science and Engineering, University of California, Berkeley (1993). Fulkerson Prize in Discrete Mathematics given jointly by the American Mathematical Society & Mathematical Programming Society (1988) Fellow of Bell Laboratories (since 1987). Texas Instruments Founders' Prize (1986). Marconi International Young Scientist Award (1985). Golden Plate Award of the American Academy of Achievement, presented by former U.S. president (1985). Frederick W. Lanchester Prize of the Operations Research Society of America for the Best Published Contributions to Operations Research (1984). President of India gold medal, I.I.T. Bombay (1978).

References

External links Distinguished Alumnus 1996 IIT Bombay Flashback: An Interior Point Method for Linear Programming IIT Bombay Heritage Fund Karmarkar function in Scilab

Worked examples

Example 1 — a first encounter with Narendra Karmarkar

Start with the simplest possible case. Write down what Narendra Karmarkar claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Narendra Karmarkar before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Narendra Karmarkar ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Narendra Karmarkar

In research: Narendra Karmarkar appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Narendra Karmarkar in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Narendra Karmarkar is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1957 births, 20th-century Indian mathematicians, 21st-century Indian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Narendra Karmarkar outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Narendra Karmarkar in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Narendra Karmarkar means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Narendra Karmarkar out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Narendra Karmarkar in simple terms?

Narendra Krishna Karmarkar (born 1956) is an Indian mathematician. He developed Karmarkar's algorithm.

Why does Narendra Karmarkar matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Narendra Karmarkar?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Narendra Karmarkar.