Thursday, March 27, 2014

Should We Have a TCS Ethics Board?

We sometimes hear of the (rare) scientist who fakes data or results of experiments. In theoretical computer science one cannot fake a theorem, particularly an important result that will attract close scrutiny before publication in a conference or journal. But that doesn't mean we don't have academic improprieties from outright plagiarism to heated arguments over who should receive credit for a result.

If these issues involve submissions to a particular conference, journal or grant they generally get resolved through the program committee chair, editor-in-chief or program officer. But often these problems go beyond a particular venue.

What if we had a TCS Ethics Board composed of a few of the most trusted members of our community? For example, if two people argue whether or not they proved the same result independently, the board could first try to come to a mutually acceptable resolution and if that fails, make an independent assessment that could be used by PC chairs and EiCs.

For more egregious cases of intentional plagiarism and/or theft of ideas, the board could write a stern letter that would go the perpetrator's supervisor and possibly recommend banning that person from publishing in various TCS journal and conferences for a specified period of time.

The vast majority of TCS researchers are quite honest and to a fault share credit for their ideas, but every now and then some researchers, probably not even realizing they are acting unethically, create an atmosphere of distrust with their actions. An ethics board would show that we care about proper academic behavior and giving a confidential forum where people can address their grievances and hopefully resolve issues before, as had happened, driving people out of our field.  

Sunday, March 23, 2014

The answer is either 0,1, or on the board

I have heard (and later told people) that the in a math course if you don't know the answer you should guess either 0 or 1 or something on the board. This works quite often.

I have heard that in a course on history of theater you should guess either
the theater burned down  or prostitution.  For example, the first musical
was The Black Crook and it happened because of a fire (see the pointer).

In upper level cell biology the guess is If only we could solve the membrane problem.

In a math talk you can always ask is the converse true? or Didn't Gauss prove that?

In computer science when someone asks me about a problem I say  Its probably NP-complete.

In Christian Bible Study a good answer is either Salvation or Jesus. These are referred to as Sunday school answers.

If you know what the usual things to say in other fields is, please comment.

Thursday, March 20, 2014

Spring Breaking at Dagstuhl






Tuesday, March 18, 2014

Leslie Lamport wins Turing Award!

Leslie Lamport wins Turing Award!
See here for more details.

Leslie did work on reliability of systems and security that
(according to the article) is ACTUALLY BEING USED. So Real People
use his stuff.

He also developed LaTeX (building on TeX) which we all know and most
of us use. Academics use LaTeX but I honestly don't know how wide spread
it is outside of academia. However, this could be the first time that a Turing award winner did something that I used DIRECTLY (I am sure I use RSA and other things indirectly).

How well known is The Turing Award? its called `the nobel prize of computer science' but I think its far less well known than the Nobel Prize.

The Fields Medal and he Mill Prize got a big publicity boost when Perelman turned them down. But that only got them 15 minutes of fame, including a Stephen Colbert segment `whose not honoring me now'. So I will not be urging Leslie Lamport to turn  down his Turing Award in order to give it more fame.


Thursday, March 13, 2014

Cosmos from Generation to Generation

During high school, well before the world-wide web with its bloggers and YouTube, out came a series Cosmos that I watched religiously. Back then you had to watch a show when it was aired and no skipping of commercials, though Cosmos was a PBS (public-broadcasting) show so it didn't have any. Cosmos was hosted by the late great Carl Sagan. While I don't remember the contents of the show so much, I do remember being quite inspired by it and the show surely played a role in my future life as a scientist.

I went to Cornell as an undergrad just a year after Cosmos' broadcast. Carl Sagan was a legend on campus, though I saw him just once, in a debate over Ronald Reagan's Star Wars plan. Sagan did have an amazing house looking out over the Ithaca gorge that you could see from the suspension bridge I crossed every day.

Now my younger daughter is in high school and Neil deGrasse Tyson takes on the difficult task of updating Cosmos for this new generation. Molly and I watched the first episode last night. (I'm still blown away we can watch when we want and skip the commercials.) It really brought back memories of the original show and I was really touched when Tyson talked about meeting Sagan as a high school student.

Tyson is giving a talk at Georgia Tech next month. Tickets went on sale yesterday and sold out within hours. Incredible to see the return of the scientific superstar.

Monday, March 10, 2014

Why do we think P NE NP? (inspired by Scott's post)

Recently  Scott Posted an excellent essay on reasons to think that P NE NP.  This inspired me to post on the same topic. Inspired is probably the right word. Some of my post is  copied and some of my post   are my thoughts. A good test: if its intelligent and well thought out then its probably from Scott.

Why do scientists believe any particular theory?  I state three reasons, though there are likely more:
(1) By doing Popperian experiments- experiments that really can fail. Their failure to fail helps to confirm the theory. This is common in Physics, though gets harder when the particles get smaller and string-like. (2) Great Explanatory power. Evolution is the main example here--- it's hard to do real experiments but one can look at the data that is already out there and find a theory that explains it all. (3) (Kuhn-light) It fits into the paradigm that scientists already have. This comes dangerously close to group think; however, if most of the people who have looked at problem X think Y, that should carry some weight.

Can we do Popperian experiments for P vs NP? For that matter can we do Popperian experiments in Mathematics? Goldbach's conjecture and the Riemann Hypothesis seem to have good empirical evidence. Though that kind of reasoning gets me nervous because of the following true story: Let li(x) = int_0^x dt/ln t.
Let pi(x) be the number of primes \le x. It is known that li(x) and pi(x) are VERY CLOSE. Empirical evidence suggested that li(x)  \le  pi(x) and this was conjectured. Skewes proved that there was an x  for which li(x) \ge  pi(x). His bound on x, the the Skewes' number ,was quite large, at one time the largest number to appear in a math paper (that record now belongs to  Graham's Number). Then Littlewood, Skewes's advisor, showed that the sign of li(x)-pi(x) changes infinitely often. So the empirical evidence was not indicative.

There might also be empirical tests you can do for continuous math, especially if its related to physics so you can do physics experiments.

Have there been Popperian experiments to try to verify P NE NP? I am not quite sure what that means, but I do not think there have been (if I'm wrong please comment politely).

So we move on to Great Explanatory Power. Are there many different empirical facts out there for which P NE NP would explain them and give a unifying reason? Does a bear... Well, never mind, the answer is YES! I give one  examples (from Scott's post) and two more. But note that there are MANY MANY MORE.

  1. Set Cover problem: Given S_1,....S_m \subseteq {1,...,n} find the size of the smallest subset of S_1,...,S_m that covers the union of S_1,...,S_m. Chvatal showed in 1979 that one can find, i poly time, a subset of S_1,...,S_m that is (ln n)+OPT. Okay, great, an approximation. EMPIRICAL FACT: people seemed unable to improve on this at all. In 2013 Dana Moshkovitz proved  that, assuming P\ne NP, this bound CANNOT be broken. Note that the algorithm of Chvatal and the lower bound of Moshkovitz have nothing to do with each other.
  2. Vertex cover: given a graph find the smallest set of vertices so that every edge has   one of them as an endpoint. There is an algorthm that gives 2OPT. There is one that does ever so slightly better: (2-(1/sqrt(log V))OPT.  In 2005 Dinur and Safra proved that, assuming P NE NP, there is no 1.36*OPT approximation. This does not match exactly but it still explains the lack of progress somewhat (more on this later when I discuss UQC).
  3. Max 3-SAT: given a 3-CNF formula find an assignment that maximizes the number of clauses satisfied.  Karloff and Zwick proved that there is an algorithm that finds an assignment satisfying (7/8)*OPT. Hastad proved that, assuming P NE NP, (7/8)*OPT is the best you can do.
A bit more prosaic: P NE NP explains why people have had a hard time solving THOUSANDS OF PROBLEMS. I am most impressed with HAM CYCLE since mathematicians had been working on that one for quite some time--- trying to get a similar char to that of EULER circuit.

So in summary, I find that P NE NP has GREAT explanatory power. That makes it a very compelling conjecture. Let us apply this test to other conjectures.

  1. Sigma_2 \ne Pi_2. Does this assumption explain anything? Our inability to find a circuit for SAT. I dont know what else it implies. Same for Sigma_i vs Pi_i. This might qualify as mini-kuhnian: Sigma_2\ne Pi_2 fits into how we view the world.
  2. P=BPP.  Almost every problem in BPP ended up falling into P over time. P=BPP would explain this. Also Nisan-Wigderson and its extensions make P=BPP fit into our world view.
  3. Unique Game Conjecture. This explains many upper and lower bounds that match, though nowhere near that of P NE NP. One of them is the constant 2 for VC. Even so, I find that compelling. (One of Scott's commenters said that all of the lower bounds from UGC are actually unified some how, so its not quite as compelling.)
  4. Factoring not in P. No real explanatory power here except that we seem to have a hard time finding an algorithm for Factoring. 
  5. Graph Isom not in P. Similar to Factoring not in P.
So, what are our reasons to think Sigma_2 \ne Pi_2?

Lastly, mini-Kuhnian. What do people in the field think? The polls on P vs NP that I conducted in 2002  and 2012 (see here)  indicate that believe that P NE NP is growing- roughly 60% in 2002, roughly 80% in 2012. Some of the commentators on Scott's blog took that 20% of P=NP people to be relevant.
And indeed some of the P=NP people are both serious theorists and also not Dick Lipton (who seems to be who  Lubos Motl points to) as a serious theorist who thinks P=NP).(ADDED LATER- SOME COMMENTERS HAVE INFORMED ME THAT LIPTON IS JUST OPEN TO THE POSS THAT P=NP. ) But some of those people emailed me that this was a protest vote, protesting the fields certainty that P=NP. I also note that three of them compared it to their voting or Ralph Nader in 2000, only with less drastic consequences.

I personally don't take `what people think' that seriously, but because of my polls we actually know what people think, so I put it out there.

Thursday, March 06, 2014

Favorite Theorems: Unique Games

Michel Goemans and David Williamson made a splash in the 90's using semidefinite programming to give a new approximation algorithm for the max-cut problem, a ratio of 2θ/(π(1-cos(θ)) minimized over θ between 0 and π, approximately 0.87856. Hard to believe that this ratio is tight, but it is assuming the unique games conjecture.
The first paper showed that the Goemans-Williamson bound was tight assuming the unique games conjecture and a "majority is stablest conjecture", the last says very roughly that the most robust election scheme is a simple majority. The second paper, which followed soon thereafter, proved an invariance property that implies, among other things, that indeed majority is stablest.

Khot and Oded Regev show that under the unique games conjecture that essentially the best algorithm for approximating vertex cover is to take all the vertices involved in a maximal matching.

Prasad Raghavendra gives a simple semidefinite programming approximation algorithm for any constraint satisfaction problem which is optimal under the UGC.

Sanjeev Arora, Boaz Barak and David Steurer describe an algorithm that given a unique game where 1-δ fraction of the edges can be satisfied, you can in time 2npoly(δ) find a coloring that satisfies a constant fraction of edges. This may or may not give evidence against the UGC.

Luca Trevisan has a nice recent survey on the unique games conjecture, covering much of the above and more, including beautiful connections between unique games and semidefinite programming.

Tuesday, March 04, 2014

Why are there so few intemediary problems in Complexity? In Computability?

There are thousands of natural PC problems. Assuming P NE NP how many natural problems are there that are
in NP-P but are NOT NPC? Some candidates are Factoring, Discrete Log, Graph Isom, some in group theory, and any natural sparse set. See
here for some more.

A student asked me WHY there are so few natural intermediary problems. I don't know but here are some

  1. Bill you moron, there are MANY such problems. You didn't mention THESE problems (Followed by a list of problems
    that few people have heard of but seem to be intermediary.)
  2. This is a question of Philosophy and hence not interesting.
  3. This is a question of Philosophy and hence very interesting.
  4. That's just the way it goes.
  5. By Murphy's law there will be many problems that we can't solve quickly.

At least in complexity theory there are SOME candidates for intermediary sets.
In computability theory, where we know Sigma_1 \ne \Sigma_0, there are no
candidates for natural problems that are c.e., not decidable, but not complete. There have been some attempts to show that there can't be any
such sets, but its hard to define ``natural'' rigorously. (There ARE sets that are c.e., not dec, not complete, but they are
constructed for the sole purpose of being there. My darling would call them `dumb ass' sets,
a terminology that my class now uses as well.)

A long time ago an AI student was working on classifying various problems in planning. There was one that was c.e. and not decidable
and he was unable to show it was complete. He asked me to help him prove it was not complete. I told him, without looking at it,
that it was COMPLETE!!!!!!!!! My confidence inspired him to prove it was complete.

So, aside from the answers above, is there a MATH reason why there are so few
intermediary problems in Complexity, and NONE in computability theory?
Is there some other kind of reason?