Computational Complexity


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Friday, April 18, 2003

The Turing Award

As noted in a comment to the last post, it is now official that Ron Rivest, Adi Shamir and Len Adleman won the 2002 Turing Award.

Unfortunately outside of computer science and particularly outside academics the Turing award is not so well known or respected. In 1987, I was a graduate student visiting my old fraternity at Cornell, Anne Marie Hopcroft came in. Anne Marie was dating one of the fraternity brothers at the time. "My father won the Turing Award! My father won the Turing Award!", she exclaimed. Nobody, besides myself, seemed the least bit interested. She and I tried to explain the importance of the award but to no avail. Had her father won the Nobel prize, you could be sure the reaction would have been different.

The 1997 movie Good Will Hunting gave great publicity for mathematics much by explaining the importance of the Fields Medal to the masses. What can we do to make the Turing Award better known?

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Tuesday, April 15, 2003


The ACM doctoral dissertation award, given to the best doctoral thesis in computer science, was awarded to Venkatesan Guruswami for his thesis "List-Decoding on Error-Correcting Codes". Another theorist, Tim Roughgarden, was one of the runners-up. This was definitely a great year for theory Ph.D. theses.

Rumors are flying that theorists Ron Rivest, Adi Shami and Len Adleman won the Turing Award for their work on the RSA cryptosystem. The Turing Award is the highest honor in computer science, the closest we have to a Nobel prize.

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Monday, April 14, 2003

Finding Problems to Work On

Often graduate students ask me for a good problem to work on. This is one of the biggest challenges of an advisor. A good problem for a graduate student must fulfill each of three characteristics.
  1. Open.
  2. Doable.
  3. Interesting.
Finding problems that fit any two of these three is not hard, but if a problem is doable and interesting, someone likely would have solved it by now. Too often interesting is the property that is given the least emphasis.

I generally give the advice that my advisor, Michael Sipser, gave to me. Pick up a proceedings of a recent conference in your area and read through the abstracts of papers until you find one that interests you. The "interests you" part is important, for without it you won't have the motivation to study further.

Read the paper thoroughly. Read related papers. If you lose interest, start the process all over again.

Once you've read several papers in an area that interests you talk about it with your advisor and your fellow graduate students. Some of these papers might list open questions and you could work on those. You might say, "Karp listed this as an open question, and if Karp can't solve it why should I be able to?" Karp is a very smart but also very busy person. It is unlikely he spent more than an hour thinking hard about these questions. As a graduate student you can spend much more time focusing on these problems and could easily make more progress than someone like Karp could.

Even better is to formulate your own problems. Perhaps there is an interesting variation in a model that the original paper, for whatever reason, did not cover. Perhaps you can find connections between two papers that no one had noticed before. These are great problems to work on: As you are breaking new ground, theorems can start flowing like water. Just remember not to have too much weirdness in your questions; keep the research interesting.

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