Computational Complexity


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Friday, October 25, 2002

Hard Problems

Occasionally someone comes to me and says, "I have a new algorithm for blah and it seems to work on all of the cases I can think of. Can you give me some real instances to test it on?" Now this is not my speciality--I would much rather see a proof of correctness of an algorithm. But for all those who think they have the next great algorithm for satisfiability, let me give you some useful links.

The first place to look is the problem instance collection of INFORMS, the Institute for Operations Research and the Management Sciences. They have links to all sorts of interesting problems like graph coloring, traveling salesman and combinatorial auctions.

For factoring, you can make some real money by solving the RSA Factoring Challenges.

For graph isomorphism, check out The Graph Database. The graph database only seems to have isomorphic graphs but a good isomorphism tester should give the isomorphism. I haven't been able to find a collection of nonisomorphic graphs that fool many isomorphism testing algorithms. See also the Nauty algorithm.

For satisfiability, there are algorithms that seem to generate hard instances. You can also take problems like graph coloring from the INFORMS site and convert them to satisfiability questions.

8:43 AM # Comments []  

Tuesday, October 22, 2002

Infinity and the Supreme Court

Don't worry loyal readers. Circumstances are making it difficult for me to write posts this week but I hope to catch up soon.

The U.S. Supreme Court is taking on a case that deals with an interesting mathematical issue. The case consists of the extension of the copyright--often called the Mickey Mouse rule since just when Disney's copyright of Mickey is about to expire, the length of the copyright is extended.

The U.S. constitution prohibits unlimited copyrights. The lower courts have said that a finite extension of a finite term is still finite. So the lawmakers are getting around the constitution by approximating the unconstitional infinite term by longer and longer finite terms. This is basically a mathematical trick--creating infinity while always locally looking finite.

Will the supreme court put a stop to this? This will be an interesting case to watch.

8:33 PM # Comments []