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Richard M. Karp

Richard M. Karp 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 Richard M. Karp rather than just read about it. In short: Richard Manning Karp (born January 3, 1935) is an American computer scientist and computational theorist at the University of California, Berkeley. He is most notable for his research in the theory of algorithms, for which he received the 1985 ACM Turing Award, The Benjamin Franklin Medal in Computer and Cognitive Science in 2004, and the Kyoto Prize in 2008.

Richard M. Karp — main illustration
Richard M. Karp — illustration

Key takeaways

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

Reference excerpt

Richard Manning Karp (born January 3, 1935) is an American computer scientist and computational theorist at the University of California, Berkeley. He is most notable for his research in the theory of algorithms, for which he received the 1985 ACM Turing Award, The Benjamin Franklin Medal in Computer and Cognitive Science in 2004, and the Kyoto Prize in 2008. Karp was elected a member of the National Academy of Engineering (1992) for major contributions to the theory and application of NP-completeness, constructing efficient combinatorial algorithms, and applying probabilistic methods in computer science.

Biography Born to parents Abraham and Rose Karp in Boston, Massachusetts, Karp has three younger siblings: Robert, David, and Carolyn. His family was Jewish, and he grew up in a small apartment, in a then mostly Jewish neighborhood of Dorchester in Boston. Both his parents were Harvard graduates (his mother eventually obtaining her Harvard degree at age 57 after taking evening courses), while his father had had ambitions to go to medical school after Harvard, but became a mathematics teacher as he could not afford the medical school fees. He attended Harvard University, where he received his bachelor's degree in 1955, his master's degree in 1956, and his Ph.D. in applied mathematics in 1959. He started working at IBM's Thomas J. Watson Research Center. In 1968, Karp became professor of computer science, mathematics, and operations research at the University of California, Berkeley. Karp was the first associate chair of the Computer Science Division within the Department of Electrical Engineering and Computer Science. Apart from a 4-year period as a professor at the University of Washington, he has remained at Berkeley. From 1988 to 1995 and 1999 to the present he has also been a research scientist at the International Computer Science Institute in Berkeley, where he currently leads the Algorithms Group. Richard Karp was awarded the National Medal of Science, and was the recipient of the Harvey Prize of the Technion and the 2004 Benjamin Franklin Medal in Computer and Cognitive Science for his insights into computational complexity. In 1994 he was inducted as a Fellow of the Association for Computing Machinery. He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences. He is the recipient of several honorary degrees and a member of the U.S. National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society. In 2012, Karp became the founding director of the Simons Institute for the Theory of Computing at the University of California, Berkeley.

Work Karp has made many important discoveries in computer science, combinatorial algorithms, and operations research. His major current research interests include bioinformatics. In 1962 he co-developed with Michael Held the Held–Karp algorithm, an exact exponential-time algorithm for the travelling salesman problem. In 1971 he co-developed with Jack Edmonds the Edmonds–Karp algorithm for solving the maximum flow problem on networks, and in 1972 he published a landmark paper in complexity theory, "Reducibility Among Combinatorial Problems", in which he proved 21 problems to be NP-complete. In 1973 he and John Hopcroft published the Hopcroft–Karp algorithm, the fastest known method for finding maximum cardinality matchings in bipartite graphs. In 1980, along with Richard J. Lipton, Karp proved the Karp–Lipton theorem (which proves that if SAT can be solved by Boolean circuits with a polynomial number of logic gates, then the polynomial hierarchy collapses to its second level). In 1987 he co-developed with Michael O. Rabin the Rabin–Karp string search algorithm.

Turing Award His citation for the (1985) Turing Award was as follows:

For his continuing contributions to the theory of algorithms including the development of efficient algorithms for network flow and other combinatorial optimization problems, the identification of polynomial-time computability with the intuitive notion of algorithmic efficiency, and, most notably, contributions to the theory of NP-completeness. Karp introduced the now standard methodology for proving problems to be NP-complete which has led to the identification of many theoretical and practical problems as being computationally difficult.

References

External links

ACM Crossroads magazine interview/bio of Richard Karp Karp's Home Page at Berkeley Biography of Richard Karp from the Institute for Operations Research and the Management Sciences

Illustrations

Richard M. Karp illustration

Worked examples

Example 1 — a first encounter with Richard M. Karp

Start with the simplest possible case. Write down what Richard M. Karp 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 Richard M. Karp 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 Richard M. Karp 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 Richard M. Karp

In research
Richard M. Karp 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 Richard M. Karp 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
Richard M. Karp is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1935 births, 20th-century American engineers, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Richard M. Karp 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.
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How to study Richard M. Karp in 20 minutes

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

Frequently asked questions

What is Richard M. Karp in simple terms?

Richard Manning Karp (born January 3, 1935) is an American computer scientist and computational theorist at the University of California, Berkeley. He is most notable for his research in the theory of algorithms, for which he received the 1985 ACM Turing Award, The Benjamin Franklin Medal in Comput…

Why does Richard M. Karp 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 Richard M. Karp?

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 Richard M. Karp.

Tags

  • 1935 births
  • 20th-century American engineers
  • 20th-century American mathematicians
  • 20th-century American scientists
  • 21st-century American engineers
  • 21st-century American mathematicians
  • 21st-century American scientists
  • American operations researchers
  • American theoretical computer scientists
  • Fellows of the Association for Computing Machinery
  • Fellows of the Institute for Operations Research and the Management Sciences
  • Fellows of the Society for Industrial and Applied Mathematics

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