Why Become a Professor

Someone took me to task because in November I posted that the CRA News had 50 pages of job ads but didn't note that very few of those ads specifically were searching for CS theory faculty. Yes, it is true that theory is not as high on the search agenda as big data and other applied areas, but many of these schools will hire theorists after they fail to find qualified applicants in the other areas. My advice is to apply widely and it's not too late to do so, as many CS departments are just starting their interview process.

Why is it so hard for universities to hire in applied CS? Because you are not just competing against other universities, you are competing against industrial labs. Besides the usual arguments of typically hire base salary and no required teaching or grants, a place like Facebook or Google can give you access to data that you just can't get a university and your research will have a real-world impact faster than basic academic research.

So why be a professor? Money isn't as big an issue as you expect, professors can consult, own significant portions of their IP (depending on the school) and can start companies. Teaching is time-consuming but extremely rewarding. To me there are two aspects that make being a professor the best job in the world.

• Freedom to set your own research agenda: Very few labs these days give you the freedom to choose your own research topics and even fewer will reward you for that. In academics we expect you to develop your own research areas and succeed in them. 
• Working with students: The relationship between advisor and advisee is not unlike a parent and child. And there's no better feeling than watching them succeed. You can often get summer interns and postdocs in industry but it just isn't the same.

When is a paper public? When is anything public?

A while back I had a paper in an intermediary stage. The version posted to my Ramsey Theory Course Website was not final. Is the paper public? I didn't think about it much but I didn't intend it to be since it was not done yet. But Adam Sheffer's Google Scholar (more on that later) didn't know that. So his Google Scholar program found the paper and he blogged about it here.

This was FINE- my co-author David Conlon posted a comment on the blog that a revised version was coming, and I asked Adam to modify the blog to say so as well. Plus, I am DELIGHTED and SURPRISED when someone noticed my work.
When the final version came out Adam DID report about it here.
But it raises the question- when is a paper public? Some related thoughts

1. (Kudos to Adam for pointing me to this one). I had heard the ABC conjecture might be solved. What I didn't quite know is that the author posted the papers on HIS OWN website, not on arXiv. Did he intend for it to go public? I do not know- but it is NOW public. If its not correct he can always say well, I didn't tell you it was ready for
   prime time yet.
   
2. A while back a student pointed me to a website with a paper that claimed to show GI is in P. The author DID NOT post it to arXiv (this may have been before there was an arXiv) nor did he email GI experts across the planet to look at it. So is it public? Is it my job to debunk it? It would be a bit odd to tell someone who didn't ask my opinion that YOUR PROOF IS WRONG! The student was hoping it was TRUE so he wouldn't have to learn the proof that if GI is NPC then PH collapses. I ended up telling the student that its surely wrong else since if GI was in P then I would known it--- not a really rigorous proof, but it sufficed. See here for more on this non-rigorous proof technique.
   
3. I have read stories of people who post personal things on FaceBook (a common one is that they are gay) and then are shocked, shocked, when their parents find out.
   
4. There's a nice song about a related issue: My Mom's on Facebook.
   
5. On the TV show West Wing there was a segment where someone thought a story was just regional and hence would not affect her confirmation hearing. She had to be told NO- there is no such thing as a story that is just regional. Journalists and others can FIND STUFF if it is out there.
   
6. Similarly to the last item: I can't post a paper just for my class because Google Scholar will find it (I DO NOT EVER require a password for a course website, I don't want to hassle the students and I am happy if somone else wants to see what I am teaching. Note also that this blog is NOT complaining that Adam found my paper). I (cordially) emailed Adam Sheffer inquiring how Google Scholar found me. For my fellow Luddites I reprint his answer (hmmm, I don't know if he meant his email to be public.)
   

   Regarding how Google Scholar works: The system constantly scans the web for new papers. It knows the papers which I have coauthored (it finds them while searching the web and asks me to verify that they are indeed mine). Then, in future scans, if it stumbles upon a paper that might be relevant to me - it sends me and update about it. I am not sure what exactly are the criteria that it uses, but it seems to be papers by my coauthors and papers on similar topics (perhaps papers that have common references with my papers?).
   

   Sound like when TIVO tried to guess what shows you liked- it could be right but it could be far off. I know of liberals who watched FOX news a lot to gain insight into what people they disagree with thought, and then their TIVO thought were Tea Partiers. Then TIVO thought they liked Tea.
   
7. I gave Adam kindly blogger-to-blogger advice: DO NOT let this be a cautionary tale. Do not ask permission to post about a PAPER --- just do it. I've done it here when blogging about Galois games and here when blogging about how much trig should a governor know. If you post on something a bit more personal (e.g., here) then maybe you should get permission (one of the people gave permission, the other never responded).
   

So what to make of all this? We are in a time of transition and some people
may end up revealing more than they intended. The next generation may learn;
however, we seem to always be in a time of transition.
"p.html" 31L, 4785C written

Analog Adventures

I was 11 forty years ago when Dungeons and Dragons first appeared and by high school many of my friends spent far too many hours embarking on those fantasy adventures. I didn't play much myself only joining a few campaigns for a short period of time. Nevertheless the game hit its mark, giving escapism to our inner nerdoms.

I just finished a new book on D&D Of Dice and Men by David Ewalt. Ewalt tells three interlocking stories: The history of D&D, Ewalt's personal journey into the game, and some campaigns he's embarked on from the characters' point of view.  Gary Gygax and Dave Arneson originally created the game but Dave soon left the company and was written out of the books. Gary mismanaged the company which has bounced around from various owners every since. I hadn't really kept up with D&D after college and I'm surprised that it has so many incompatible versions (reminds me of LaTeX and Python). A fifth version of D&D to unite them all is due for release this summer.

My daughter's school just put on a production of She Kills Monsters, a play about a woman who discovers her late sister through the sister's D&D adventures. My daughter played an evil cheerleader and her line "We're way too powerful for you" reminded us both of her classic role as NP.

These days we have immersive rich interactive games on our Play Stations and smart phones but still there is still nothing like gathering around a table transformed into a tavern as we meet our fellow adventurers and embark on the next quest.

Maryland looking for a Lecturer/Who teachers your intro courses?

My chairman, Samir Khuller, asked me to post our job posting for a lecturer to my blog, so I and doing it right now. I think he overestimates the power of this blog.

At Univ of MD at College Park lecturers teach most sections of our intro sequence (CS1, CS2, CS3, Discrete Math). They might sometimes do a higher level course if the need arises. They are there to mostly teach and advise students, not do research, though some do and that's certainly fine. Some have PhD's and some don't.  Note that this is a full time job--- these are not adjuncts or rent-a-profs. They are part of the department.

Is having lecturers teach the intro courses  a good idea? Overall YES; however, I would like to have professors teaching those courses once in a while, or be involved once in a while, as they may have a good idea to share with the lecturer (then again, they might  not).  Having said that, you don't see me volunteering for CS1, CS2, or CS3 (My policy: I never teach a course where I would get a B if I took it. One exception- I did once teach Graduate Algorithms and got in a bit over my head.) I do teach Discrete Math once in a while. I also like to proofread the midterm and final of whoever is teaching it. I'm NOT that good a proofreader, but I like to know what they are up to and it gives me an excuse to talk to them about the course and make sure it doesn't drift to much. I would like to think I have a good rapport with the lecturers.

Does having a PhD in CS and being a professor give one some insights on what should be in CS1,2,3 and how to teach it? I honestly don't know. My first semester at Univ of MD (1985) we were teaching program verification in CS1. I knew immediately it was a bad idea and eventually (without any input from me) the dept stopped doing that. This is a case where being a researcher may be a negative with regard to education.

I would like to think that my working in theory helps me teach Discrete Math.  It does as a source of some problems (e.g, if a paper says `by an easy induction...' that can be a problem set) but one should not get to carried away and go over their heads.

IEEE and the Conference on Computational Complexity

Dieter van Melkebeek, current conference chair of the IEEE Conference on Computational Complexity has set up a forum to discuss the future affiliation of the conference. Read over the manifesto and update. You can give general comments on the about post. Dieter discusses three options:

1. Remain with IEEE
2. Have a joint ACM/IEEE conference in some fashion.
3. Become an unaffiliated conference.

For most of you this shouldn't matter at all. Most of you readers have never attended the complexity conference (though you ought to give it a try sometime) and those that do would probably continue attending no matter who sponsors the meeting.

There has been a go-it-yourself tendency in this field so as not to pay any organization fees and to publish papers in an open-access format. Just realize this approach has some potential downfalls.

• Without a sponsor, the conference and in particular the organizing committee, is fully responsible for any deficit. One bad hotel contract can sink a conference. To guard against this, you'll need to budget a surplus far larger than IEEE or ACM would require. Also IEEE and ACM can use their influence to get better deals such as on hotels. 
• You'll need considerably more volunteer time from faculty to handle the larger administrative load. This time doesn't show up in the financial calculation but it is a real expense.
• Having a sponsoring organization gives a set of checks and balances to guarantee that the conference retains a consistent mission and be fiscally responsible. If a conference is solo and the organizing committee drops the ball, the conference just disappears. 

I'm not recommendation here, just trying to point out some pitfalls that usually don't get discussed. I'll stay out of the actual debate on the future sponsorship of CCC and leave that to the younger generation.

Superbowl underdogs and overdogs

(Stephen Colbert tells me that NFL guards their copyright of the name of the game they played on Sunday, which is why stores say they have a `big game sale on beer'. I will get around this the same way he does. I hope he doesn't sue.)

In Superb owl XLVIII (48) (one of the few uses of Roman Numerals left) Denver was the favorite but got beaten. This is not so unusual and they were not a favorite by much-just 2.5 points. But they lost 43-8. That sounds unusual--- for the favorite to get completely whomped (spellcheck thinks that's not a word, but spellcheck doesn't even think spellcheck is a word).

So- how uncommon is it for the favorite to get whomped? We would need a rigorous definition of whomped. I'll say two touchdowns, or 14 points. A list of all of the superb owl games and what the spread was and what happened is here. I summarize:

1. The underdog WON 15 times. The most surprising was probably when the NY Jets were an 18-point underdog to the Baltimore Colts  in Supeb owl III in 1969 and won 16-7. Good thing they won since Joe Namath (the NY Jets QB) guaranteed  victory.
2. In 2010, Superb owl 44,  Indianapolis was a 5 points favorite over the New Orleans Saints but the Saints whomped  31-17.
3. In 2003, Superb owl 37,  Tampa Bay was a 4 point underdog to Oakland. Tampa Bay whomped by winning 48-21.'
4. In 1988, Supeb owl 22, Washington was a 3 point underdog to Denver, but Washington whomped 42-10.
5. In 1984, Superb owl 18, LA was a 3-point underdog to Washington, but LA whomped 38-9.
6. In 1981, Superb owl 15, Oakland was a 3 point underdog to Philadelphia, but Oakland Whomped 27-10.
7. In 1970, Superb owl 4, Kansas City was a 12 point underdog to Minnesoda, but whomped 23-7.  The reason they were an underdog is that people still though the AFC to be the lesser league and didn't remember that in Superb Owl 3 the AFC won (though didn't whomp).

So the underdog has whomped 5 times. That is FAR MORE than I would have thought. Does this show that underdogs are undervalued? Not sure since if an underdog wins it doesn't matter by how much for the betting, where as if a favorite wins it matters by how much for the point spread.

This may also call into question if point-spread is the best way to express `this teams is that much better than that team'. One issue (though it was NOT an issue in Superb owl 48) is that if a team is behind
then they may use a high-risk high-reward strategy which, if it fails, they lose my a lot. The phrase one may hear is ``the game was closer than the score''.  Note that for baseball they don't do point spreads, they do odds instead. Should Football follow that? What are the PROS and CONS of points spread vs odds?

The cliche is `I watch the game for the commercials' I actually skip the game and watch the `best of superb owl commercials' that come the week before the game.

Favorite Theorems: Connecting in Log Space

We start the favorite theorems with a result that might surprise many is still less than ten years old.

Undirected Connectivity in Log-Space by Omer Reingold (PDF)

Intuitively, this result says you can tell if two points are connected in a complex maze by only having to remember the equivalent of a constant number of locations in the maze. Reingold's algorithm builds an expander graph based on the zig-zag construction in a very clever way that uses very little space to construct and to check that two points connect.

In 1979, Aleliunas, Karp, Lipton, Lovász and Rackoff showed that one can solve s-t connectivity in randomized logarithmic space by taking a random walk on the graph. My last favorite theorem from 2004 talked about derandomizing space algorithms and before Reingold the best algorithm for s-t connectivity required log^4/3 space. Indepently of Reingold, Vladimir Trifonov gave a O(log n log log n) space algorithm for s-t connectivity, a victim of bad timing.

One neat implication of Reingold's result is a new and simpler characterization of log-space as the set of problems expressible in first-order logic with ordering and symmetric transitive closure.

After Reingold's result we might have expected solutions to a number of related problems but we didn't see much progress.

• Can every randomized log-space algorithm be derandomized in log space?
• Do there exist log-space computable universal traversal sequences? 
• Can we solve directed s-t connectivity better than Savitch? 
• Can we modify Reingold's algorithm to bring log space into NC¹?

Contribute to the Martin Gardner Centennial

Dana Richards emailed us about a place to write how Martin Gardner influenced you. You can leave such comments here.  I left a comment there, but I expand it for this blog entry.

When I got interested in mathematics in high school I went to the public library looking for math books (this was before Al Gore invented the internet). I found some books by Martin Gardner and began reading them. They were just right for the level of math I was on at the time. My very first proof that I read on my own (outside of a class) was in those books- the proof that (in the terminology I use now) a graph is Eulerian iff every vertex has even degree.

I  learned about SOMA cubes (I bought a set and did every puzzle in the book in about 2 days.This is the only evidence that as a kid I was good at math). I learned the unexpected hanging paradox which confused me then (and still does). I learned the hercules-hydra game and other games that go on for a LOOOOOOOOOONG time. They are related to things in logic. I also learned about NIM games which I have used as a starting point for several student projects.

There have been some conferences in his honors, the Gathering-for-Gardner. I had the pleasure of reviewing some of the books from it. (My review is here.) These articles show that while his work was recreational this is not a well defined term- some if relates to very important and deep mathematics, and some deep math has arisen from such problems. The books also have articles about Gardner the Magician.

In  the 2000's some of his books were reprinted and I was asked to review them for my SIGACT News book review column.  I took this opp to do a joint review of several math recreational books. What a delight to reread his books and contrast them to those of his successors. And I STILL learned some math that I didn't know from them. (My review is here.)

Shortly before a column appears I always email the authors-of-books, authors-of-reviews, and publishers a first draft of my column. His publisher told me that he didn't use email (he was in his 90's!) so I postal mailed him my review. He read it, corrected some typos, but otherwise was quite happy with the review. He died a few months later. I was happy to have some contact, albeit short, with the man who helped keep me interested in math in high school and beyond.

Snow Days

An unexpected snowstorm hits the city in the middle of a workday. The roads get hopelessly clogged and I'm lucky to get home--many others just abandoned their cars, or slept in them. I'm talking about Valentine's Day, February 14, 1990 in Chicago. But the same story hit Atlanta yesterday. One big difference--Georgia Tech is closed today and tomorrow because the city can't handle the ice. The University of Chicago was open on February 15th. 

When these events happen, people wonder about the planning. Was it wise for all schools and businesses to shut down about the same time, early yesterday afternoon? Lots of blame to go around (and having CNN based in Atlanta guarantees coverage) but it is not clear that any plan would have done much better--how do you get millions of people safely home with dangerous roads and a limited public transit system? One of these times you wish P = NP and you can just find the right algorithm. One of the issues is that freak mid-day snowstorms don't happen that often, the last major one in Atlanta was 1982.

Meanwhile back in Chicago, schools were closed earlier this week, not for snow but for cold. But it was that cold on a regular basis back in the 90's. Global warming has changed expectations, as so brilliantly illustrated in this xkcd. 

Fermat's Last Theorem and Large Cardinals. Really!

A brilliant math ugrad at UMCP, Doug, is also a creative writer who
wants to work on large cardinals. His creative writing may help him there.
We had the following conversation:

DOUG: The proof of Fermat's last theorem depends on the existence
of certain large cardinals and hence is not in ZFC.

BILL: That is not true.
DOUG: Have you read the proof?
BILL: No, however, if that were true I would know it. See this blog entry.
DOUG: Why would you know it?
BILL: If FLT required LCs then

a) Number theorists would be nervous.
b) Logicians would be ecstatic
c) The math community would not have announced to the world that FLT was solved.
d) Wiles would not have collected his prize money for solving it.
e) Again, I would know it.

DOUG: All compelling arguments. Even so, FLT requires LCs.
BILL: I will bet you five dollars that the current proof of FLT does not depend on LCs.
DOUG: Uh. Your counter arguments are compelling.
BILL: So... no bet?
DOUG: Uh. No.

The next day I got an email from Doug with the subject heading

        I cheated myself out of five dollars.

 Doug found this article, What does it take to prove Fermat's Last Theorem? Grothendieck and the logic of number theory by Colin McLarty, from 2009.The article says that YES the  current proof of FLT DOES depend on LCs. Note that the proof is quite long and uses lots of other stuff that is sort of buried in it. So--- whats the catch?Why aren't number theorists nervous and logicians ecstatic? According to the article anyone who reads the proof of FLT and wanted to could unwind it  and get it down to ZFC (and likely down to PA). But nobody has bothered yet.Hence nobody is nervous or ecstatic.

I will take their word for it, but it does make ME nervous. NOT about FLT which I am sure enough people have looked at (and looked at the background literature) that it really can be made to work in ZFC.I am more worried about papers that are not quite so looked at as having LC assumptions that are hidden from the reader that cannot be easily removed.

However KUDOS to Doug for telling me something in math that I did not know and should have.  I will treat him to a more-than-five-dollar-lunch.

Postscript: AH, the article was right: FLT was proven using ordinary set theory last year. (See here) by Colin McLarty (I assume its the same person). I will still take Doug to lunch- in a stupid, pedantic, technical sense I was right- the current (2014) proof of FLT did not use LC. But for the real issue of there being any problem at all, I was clearly wrong. Only a logician would say I was right. Hmm- Doug is a logician. Its up to him. (Hmm- my spell checker allows `Hmm' but not `Hmmm')

What will we wrought?

When I went to college in the early 80's, students protested against college endowments invested in companies that had business in apartheid South Africa. My mother worked as a statistician for one of those companies. An interesting dilemma, do I support a policy that hurts the company that is indirectly helping to put me through college?

Now my daughter is in college and worrying that the computing revolution will make it hard to find a job once she graduates and making her consider those job prospects in the major she chooses. And what am I? Chair of a computer science department that helps push that revolution forward.

Computing gets quite a bit of blame these days for the widening income gap between the have and the have nots, and jobs taken over by automation, but without causing a corresponding need for other types of jobs, other than those that serve computation itself. Are those fears real? We can't answer that question yet, positively or negatively. Time will tell.

For now, we just need to do our jobs, making computing better but also understanding and mitigating the negative effects of computing. We need to make sure that computing technology becomes a growing sea that raises all boats, and not just making the world better for the technological elite.

While I stand in awe in how computer science has changed the world, I hope we don't ever end up with CS leaders getting together and saying "What have we wrought?"

We don't care about Ballroom Dancing. Should we?

YOU got into your undergrad school because not only were you good at Math but you were on
the Fencing Team and in the Latin Club (so you could taunt your opponents in Latin: ouyah allcay athay an alestrabay!). Also you had a letter from your principal who never had you for a class but can comment on your leadership since you organized a pep rally for the football team. Why does UNDERGRAD admissions care about these things? Because, while they want good students, they also want to build a community of scholars of different interests and abilities.

YOU apply to grad school in Computer Science. Hey, it worked once maybe it will work again! You write about being in the ballroom dancing club and you have a letter from the Dean, who never had you in a class,
but you worked in his office and he can attest that you are a good leader and a hard worker.

Does the admissions committee care? NO. The only things we care about are CS, MATH, and RESEARCH. A letter from someone not in math or science is worthless. Some exceptions and thoughts:

1. If you recorded ballroom dancing and made a project out of how to teach it using some interesting new technology this IS good. This is likely an Human-computer-interaction project; however, I would care about this no matter what field you are going into.
2. If you have an interest in Nat Lang Proc and know Linguistics I would care.  I would think that knowing a foreign language would also be good.
3. If you are going to go into Human computer Interaction then Psychology helps.
4. If you are going to do Quantum Computing then Physics is good. However, whatever you do Physics is good as its more evidence of math ability.
5. For ugrad its been said that if your parents are powerful OR donors you may have an easier time getting into some UGRAD schools. What about Grad school? I've honestly never seen a case of this so I honestly don't know. 

I know a student who is an excellent math major but also a creative writer. I doubt this will help him.
but should it?

I once saw in a students application a letter from his preacher attesting to his fine moral character.
Do we care? should we? How about the other way around- if someone was an EXCELLENT programmer and math person but served 8 years for armed robbery would we care? This might not be fair since perhaps he reformed.

but my real question is- for grad admissions we don't care about Ballroom Dancing or other misc.
Is this a mistake? If someone was NOT as good at math BUT a better writer, should we take them?

Favorite Theorems: Introduction

I was invited to give a talk at the FST&TCS conference held in December 1994 in Madras (now Chennai). As I searched for a topic, I realized I was just finishing up my first decade as a computational complexity theorist so I decided to recap the past decade by listing My favorite ten complexity theorems of the past decade (PDF). Not so much to choose winners, but use the theorems to survey the great research during those past ten years.

In 2004, I repeated the exercise in my then young blog for the years 1995-2004. In 2005, I went back in time and chose my favorite theorems from the first decade of complexity (1965-1974) and in 2006 I covered 1975-1984, completing the backlog of the entire history of computational complexity.

Now in 2014 we start again, recapping my favorite theorems from 2005-2014, one a month from February through November with a recap in December. These theorems are chosen by a committee of one, a reward only worth the paper they are not written on. I choose theorems not primarily for technical depth, but because they change the way we think about complexity. I purposely choose theorems with breadth in mind, using each theorem to talk about the progress of a certain area in complexity. I hope you'll be presently surprised by progress we've made in complexity over the past decade.

A short History of Crypto

I taught a 3-week summer course to High School Students called

Computer Science: A Hands Off Approach

which did some theory. One thing I did was the following storyline:

1. Shift Cipher
2. Affine Cipher
3. Gen perm cipher (any perm of a,b,c,...,z
4. PROOF that perm is unbreakable: Eve has to go through all 26! possibilities
5. PROOF that perm IS breakable: Freq analysis. Moral of the story: Any proof that a system is unbreakable makes some assumptions that Eve might not agree to. Hence proving security is tricky.
6. Matrix Ciphers. PROOF that if you use a big enough matrix its unbreakable. Sort-of true for ciphertext only (though I doubt really proven). PROOF that requires going through all possibile nxn matrices that have det rel prime to 26 to crack it using plaintext only. PROOF that this is NOT true (I leave that to my reader).
7. Vig Cipher. Proof that its unbreakble, Proof that you can break it

I was very happy with this since it really instilled in them that proofs of security are nontrivial and always have assumptions. That does not mean they are not worth anything, but you want to get the assumptions explicit to if (or even WHEN) the system is broken, you can see what assumption needs to be attended to for the next iteration. One caution- these were VERY GOOD students so they GOT IT. They didn't mistake the false proofs for real ones.
(NOTE-- I never teach the cows paradox - all cows are the same color- when
doing induction since half the class will think induction can prove anything and the other half will think that all cows are the same color.)

I then encapsulated all of this with what I call A SHORT HISTORY OF CRYPTO:

 For i=1 to infinity
                Alice and Bob: We have a cipher that nobody can crack
                Alice and Bob: We have PROVEN that it can't be cracked
                Eve: I just cracked it
                Alice and Bob: Whoops.


(I later did Diffie-Hellman in the class which I will talk about in a later blog.)

Is Traveling Salesman NP-Complete?

[Nina Balcan asked me to mention that the COLT submission deadline is February 7]

Jean Francois Puget writes a controversial post No, The TSP Isn't NP Complete which I discovered during a lengthy twitter discussion with Puget and Peter Cacioppi.

There is a well-known technicality for the Euclidean Traveling Salesman problem but let's focus instead where we are given a complete graph weighted with positive integers. One version of TSP is truly NP-complete

TSP Decision: Given an integer B, is there a cycle through all the vertices such that the total weight of the edges used is at most B?

TSP Decision is in NP by guessing the cycle and hardness by a simple reduction from Hamiltonian Cycle.

Puget's makes the point that we normally think of the TSP problem as an optimization question

TSP Minimization: Find the cycle through all the vertices that minimizes the total weight used.

TSP Minimization is not even a decision problem. In the 80's, Mark Krentel created a complexity class OptP to capture optimization problems and showed that TSP Minimization is Opt-P-complete.

One can use TSP Decision to solve TSP minimization by doing binary search, so they have effectively have the same complexity.

Puget points out that even if we are given a tour, checking that it is the shortest tour is not believed to be in NP. That problem is in co-NP and I'm guessing co-NP-complete. [Update 3/20: I was right]

Puget doesn't like when people claim TSP is NP-complete when they are talking about the optimization problem. For example from my P v NP survey

The NP-complete traveling salesperson problem asks for the smallest distance tour through a set of specified cities. 

I'm far less bothered than Puget. Those who understand the technicalities of NP-completeness know that one has to convert the optimization problem to an appropriate decision problem to formally get an NP-complete set. Others aren't led too far astray, for we do have an equivalence that P = NP if and only if there is an efficient (polynomial-time) algorithm for TSP Minimization.

Tell me more about Alice and Bob

A while back my parents were in town on a weekend when I was scheduled to give a talk to HS students who had done well on the Maryland math competition. Logistics dictated that my parents goto the talk. (They were both English majors and wouldn't like me using the word `goto' since its not a word. Fortunately they don't read this blog and see what else I do to the English Lang.)
I gave a talk on Communication Complexity (slides are here) where I did the following:

1. I stated the problem: Alice has x, Bob has y, both strings of length n. They want to know if x=y without too much communication.
   
2. I noted that they can easily solve this with n+1 bits of communication and raised the question of Can They Do Better?
   
3. We discussed this. Someone mentioned average case (informally), which helped me clarify the problem. Someone else suggested sending the number-of-1's and if it didn't match they weren't equal, but also noted that if they did--- weren't sure. Most thought that one COULD do better or else I wouldn't be talking about it.
   
4. I tell them that NO you can't do better (I do not prove this).
   
5. I told them about mod arithmetic and how in mod p, p a prime, poly of degree d have at most d roots.
   
6. I presented the O(log n), error 1/n, randomized protocol for equality that uses polynomials mod p.
   
7. I briefly talked about comm complexity in general.
   

The talk went well. It is a good topic for good HS students, and if you want to borrow my slides you can (you may need to update the political reference). Having not understood ANY of the talk Mom had the following question:
MOM: Alice and Bob-- are they married?
BILL: Oh. I'll say no.
MOM: If they are not married then how come they have such a hard time communicating?
DAD: (he didn't say anything but I could tell he agreed).

Two cheers for the Pardon of Turing. But not three.

As I am sure readers of this blog know Alan Turing was prosecuted for homosexuality in 1952, forced into hormone treatment, and committed suicide in 1954 (I had always heard that that was WHY he committed suicide
though the dates don't quite line up--- at that time he seemed to be recovered form the ordeal. So there are some legit questions about this.)

He was recently given a Royal Pardon. While I am glad he was pardoned this does raise some questions. Lets me logical.

1. If we believe the law criminalizing homosexual acts was unjust (as I am sure that all of my readers do) then Turing is a red herring- they should pardon ALL people convicted. AND note that  according to this there are 15,000 men who were convicted of this crime who are still alive.
2. Pardon means that the person didn't do the crime. This is not the case here. However, laws are supposed to promote justice, not block it.

Here is hoping that the Pardon of Turing will lead to a general pardon.

(NOTE- the pointer in item 1 says more of what I wanted to say, but says it
more elegantly than I ever could.)

2013 Complexity Year in Review

The complexity result of the year goes to The Matching Polytope has Exponential Extension Complexity by Thomas Rothvoss. Last year's paper of the year showed that the Traveling Salesman Problem cannot have a subexponential-size linear program formulation. If one could show that every problem in P has a short polynomial-size LP formulation then we would have a separation of P and NP. Rothvoss' paper shoots down that approach by giving an exponential lower bound for the polynomial-time computable matching problem. This story is reminiscent of the exponential monotone circuit lower bounds first for clique then matching in the 1980's.

If you expand to all of mathematics, one cannot ignore Yitang Zhang's work showing the liminf of the difference between consecutive primes is a constant. Dick and Ken have other great results for the year.

A big year for theoretical computer science. Silvio Micali and Shafi Goldwasser received the ACM Turing Award. The P v NP problem makes a prominent appearance on a major US television series. We are seeing the rise of currencies based on complexity. Large-scale algorithms, cryptography and privacy play center stage in the Snowden revelations on the National Security Agency.

Generally good news on the funding and jobs front in the US. After a year of sequestration and a government shutdown, looks like some stability for science funding now that congress has actually passed a budget. Plenty of theorists got academic jobs last spring and given the number of ads, this year's CS job market should be quite robust as well.

A year for books. Of course my own Golden Ticket as well as Scott Aaronson's Democritus and Tom Cormen's Algorithms Unlocked.

An odd year for the blog in 2013 without a single obituary post. Nevertheless let us remember 4-Colorer Kenneth Appel, Georgia Tech Software Engineering Professor Mary Jean Harrold and Wenqi Huang who led the Institute of Theoretical Computer Sciences at the Huazhong University of Science and Technology. In 2013 we also said goodbye to Alta Vista, Intrade, Google Reader and the CS GRE.

In 2014 we'll have the next installment of My Favorite Ten Complexity Theorems of the Past Decade and the centenaries of George Dantzig and Martin Gardner. Enjoy New Years and keep reading.

To Write, or Not to Write, That Is the Question

Guest post by Vijay Vazirani

Our field has been blessed with some great books: classics such as Knuth's volumes and Garey & Johnson literally got the field going, and the books of Lovász brought much clarity in difficult, important areas. The new millennium brought a plethora of new books by famous TCS researchers including Arora, Barack, Goldreich, Kleinberg, Nisan and Tardos. With an astonishing 33 short titles in theory, Now Publishers has virtually created an assembly line for producing books.

Even so, when faced with the prospect of writing a new book, I am filled with trepidation and self-doubt: Am I up to the effort needed? Do I have a genuinely new point of view to expound? If so, have I figured out the "right'' format and style for expounding it in the simplest and clearest manner?

The issue arose when I decided to co-teach, with my able postdoc Ruta Mehta, the course Equilibrium Computation in Spring. With her characteristic enthusiasm, Ruta has practically forced me into a long-term commitment of writing a book on this topic. However, knowing what it takes, so far I have managed to resist an unequivocal "yes".

Most people would say it is a losing proposition -- the gains are typically minuscule compared to the toils. So why do so many people write books? I can imagine several reasons, but best to leave this discussion to my esteemed colleagues who are probably yearning for something to ponder on in this holiday season ...

That brings me to another question, "Are some of the books written in this millennium eventually going to be regarded as classics in the style of Knuth or Lovász's books?'' One could look at citation counts or average citations per year to get an "objective'' reading of the situation. However, when one is talking about true class, such crude estimators are clearly not the way to go.

Your thoughts are eagerly sought ...

Our Journal is 99 44/100 percent pure!!

Sometimes we are asked to evaluate how good a journal or conference  formally(Excellent, Very Good, Good, Fair, Better-than-being-poked-by-a-stick,pass the stick). Sometimes we talk about these things informally (ICALP is the European STOC! SODA is as hard to get into as FOCS!, CCC is a topTier topics-conference!)


But is there a way to judge these things formally? And should there be?Be aware of Goodhart's Law:

When a measure becomes a target, it ceases to be a good measure.

 One way to measure how good a journal or conference is  impact factor which is based on number-of-citations. Does this work well? Some issues:

1. Even with an honest effort these things are hard to do well. People may cite the conference version, the journal version, the arXiv version, or just give a website.
2. Even with an honest effort just a few articles can skew the results.
3. Its hard to compare cross-fields.  I suspect that pure math journals have lower citations rates than biology journals.
4. If an author cites himself, should that count?
5. The above points were all about HONEST efforts. Could a journal do things to boost its impact factor and then brag about how high their impact factor is? Would they? Alas yes, see this article and this article.

So what are we left with? We could just go on our gut, but that favors journals that used to be good and aren't any longer. But the problem is deeper than all that--- can't we just say Thats a good article  and not have to proof it by saying where it was published? Alas no- all fields have gotten specialized that we must use these proxies to inform us.

 I COULD rant that we should all be well rounded enough to read outside of our field, but I know how hard that is.

I COULD rant about the dishonesty pointed out in the above links, but that's only part of the problem.

I COULD say What do you think? so I will.