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Longstanding problem put to rest:Proof that a 40-year-old algorithm is the best possible will come as a relief to computer scientists.

By Larry Hardesty


CAMBRIDGE, Mass. – Comparing the genomes of different species — or different members of the same species — is the basis of a great deal of modern biology. DNA sequences that are conserved across species are likely to be functionally important, while variations between members of the same species can indicate different susceptibilities to disease.

The basic algorithm for determining how much two sequences of symbols have in common — the “edit distance” between them — is now more than 40 years old. And for more than 40 years, computer science researchers have been trying to improve upon it, without much success.

At the ACM Symposium on Theory of Computing (STOC) next week, MIT researchers will report that, in all likelihood, that’s because the algorithm is as good as it gets. If a widely held assumption about computational complexity is correct, then the problem of measuring the difference between two genomes — or texts, or speech samples, or anything else that can be represented as a string of symbols — can’t be solved more efficiently.

In a sense, that’s disappointing, since a computer running the existing algorithm would take 1,000 years to exhaustively compare two human genomes. But it also means that computer scientists can stop agonizing about whether they can do better.

“This edit distance is something that I’ve been trying to get better algorithms for since I was a graduate student, in the mid-’90s,” says Piotr Indyk, a professor of computer science and engineering at MIT and a co-author of the STOC paper. “I certainly spent lots of late nights on that — without any progress whatsoever. So at least now there’s a feeling of closure. The problem can be put to sleep.”

Moreover, Indyk says, even though the paper hasn’t officially been presented yet, it’s already spawned two follow-up papers, which apply its approach to related problems. “There is a technical aspect of this paper, a certain gadget construction, that turns out to be very useful for other purposes as well,” Indyk says.

Squaring off

Edit distance is the minimum number of edits — deletions, insertions, and substitutions — required to turn one string into another. The standard algorithm for determining edit distance, known as the Wagner-Fischer algorithm, assigns each symbol of one string to a column in a giant grid and each symbol of the other string to a row. Then, starting in the upper left-hand corner and flooding diagonally across the grid, it fills in each square with the number of edits required to turn the string ending with the corresponding column into the string ending with the corresponding row.

Computer scientists measure algorithmic efficiency as computation time relative to the number of elements the algorithm manipulates. Since the Wagner-Fischer algorithm has to fill in every square of its grid, its running time is proportional to the product of the lengths of the two strings it’s considering. Double the lengths of the strings, and the running time quadruples. In computer parlance, the algorithm runs in quadratic time.

That may not sound terribly efficient, but quadratic time is much better than exponential time, which means that running time is proportional to 2N, where N is the number of elements the algorithm manipulates. If on some machine a quadratic-time algorithm took, say, a hundredth of a second to process 100 elements, an exponential-time algorithm would take about 100 quintillion years.

Theoretical computer science is particularly concerned with a class of problems known as NP-complete. Most researchers believe that NP-complete problems take exponential time to solve, but no one’s been able to prove it. In their STOC paper, Indyk and his student Artūrs Bačkurs demonstrate that if it’s possible to solve the edit-distance problem in less-than-quadratic time, then it’s possible to solve an NP-complete problem in less-than-exponential time. Most researchers in the computational-complexity community will take that as strong evidence that no subquadratic solution to the edit-distance problem exists.

Can’t get no satisfaction

The core NP-complete problem is known as the “satisfiability problem”: Given a host of logical constraints, is it possible to satisfy them all? For instance, say you’re throwing a dinner party, and you’re trying to decide whom to invite. You may face a number of constraints: Either Alice or Bob will have to stay home with the kids, so they can’t both come; if you invite Cindy and Dave, you’ll have to invite the rest of the book club, or they’ll know they were excluded; Ellen will bring either her husband, Fred, or her lover, George, but not both; and so on. Is there an invitation list that meets all those constraints?

In Indyk and Bačkurs’ proof, they propose that, faced with a satisfiability problem, you split the variables into two groups of roughly equivalent size: Alice, Bob, and Cindy go into one, but Walt, Yvonne, and Zack go into the other. Then, for each group, you solve for all the pertinent constraints. This could be a massively complex calculation, but not nearly as complex as solving for the group as a whole. If, for instance, Alice has a restraining order out on Zack, it doesn’t matter, because they fall in separate subgroups: It’s a constraint that doesn’t have to be met.

At this point, the problem of reconciling the solutions for the two subgroups — factoring in constraints like Alice’s restraining order — becomes a version of the edit-distance problem. And if it were possible to solve the edit-distance problem in subquadratic time, it would be possible to solve the satisfiability problem in subexponential time.

Source: MIT News Office

Fake diploma scandal: Why we need to seriously address it?

By Syed Faisal ur Rahman


 

Recent scandal related to a Pakistani software company Axact’s alleged involvement in selling fake degrees has shocked the whole country especially IT industry, media related circles and academia. The story published on 17th May 25, 2015; in The New York Times written by Declan Walsh was not just another exposé about a criminal activity happening somewhere.

The story basically jolted the foundations of our developing IT industry which relies heavily on outsourcing. It also raised questions about the standards of academic integrity and how as a society we give importance to it. I am not interested in passing judgments over Axact’s credibility or their involvement in the alleged scam but my focus is on highlighting the importance of solving it with utmost seriousness and transparency.

We are a small economy of the size of roughly 232 billion dollars which is lesser than many countries with less than half of our population. We are stuck in over a decade long warfare and our industry has faced the worst of it. In the past few years our Software and other IT related industries have provided some hope for our aspiring entrepreneurs to achieve their dreams and show the world that they are more than suspected terrorists.

Scandals like the diploma scandal, if not handled seriously will cast doubts over the credibility and ethics culture in our IT industry which will eventually result in the loss of international clientage confidence. Our aspiring young engineers and technologists are now making some serious contributions in mobile applications, game development, e-commerce, cloud computing and many other related areas. It will be unfair for them if our government simply tries to put the issue under the carpet using delaying tactics and leave the question mark on our industry’s credibility unaddressed.

The bigger issue in my view however is related to academic integrity and how we see it as a society. Few years ago, the issue of fake MNA/MPA degrees has damaged the reputation of our education sector all over the world. As a result, students and professionals who want to go abroad, now go through some serious scrutiny process which is really embarrassing and time consuming. It becomes more painful when we see that people from various other countries do not need to go through such painstaking process. If, in any way, comes out that our government officials are involved in any capacity in covering up the issue then whatever credibility is left of our academic sector will suffer too.

Also, we should keep our eyes open to see if the issue is being used for some other motives. The recent statement by one of our federal ministers linking Axact issue with absence of cyber crime law should also be seen with a great concern. Mixing two different issues like the proposed controversial cyber crime bill and this diploma scam will worsen the situation and can create more panic in our local IT industry.

The need is to investigate and prosecute the issue with highest professional standards and transparency so that we can prove to our-selves (not just the world) that we believe in fair play especially when it comes to the most respected field of education.

At the same time, I will urge Axact and its affiliate institution BOL that if they feel that they have been falsely targeted as a result of some conspiracy then they should file a lawsuit against The New York Times instead of using social media to clear their image.

 


The article is also available on Daily Times website with slight editing.