MohammadTaghi HajiAghayi on David Johnson

More than a week ago, I heard the very sad news that David Johnson has passed away after one year fight with cancer. I felt that I should write a memorial note for him. Indeed I have done the same for Mihai Pătraşcu in the same blog and both Mihai and David were very similar to me from several aspects: both were my colleagues at AT&T and more importantly my dear friends, both they got their Ph.D. from MIT (the same place that I got my Ph.D. as well), they both were extraordinary researchers, and both passed away due to cancer after almost a year-long fight with it (and I was closely aware of their situations in that year). Indeed David read my memo for Mihai and he told me that he liked it. In addition, there is another reason that I feel respect for David; he was just a bit older than my father who also passed away very recently. So here I would like to put my thoughts into words for David (and this took me more time in this case since I wanted to mention some new thoughts given the comments already in this blog). To do so, I would like to mention some of David’s personal characteristics that I appreciated a lot and give some examples on them from my interactions with him. Indeed I have even mentioned some of these to him when he was alive and told him because of these (and other reasons), I am always proud to mention that I have him as my boss at some point in my career.

First of all, David was very humble and modest especially given his extraordinary CV: he won several awards especially Knuth prize, he is the co-author of one of the top most-cited books in CS, he was fellows of almost every community that he was involved with (e.g., ACM, SIAM, AT&T), he was a member and the chair of several prestigious award committees (like Gödel, Knuth, ACM Kanellakis, ACM Thesis Award) and indeed he was a founder of some of them (e.g., Kanellakis), and he was the founder of SODA, the best algorithms conference, among others. Despite all this he was a very humble and modest man and I think lots of people who interacted with him will fully agree on this. Just to give an example, in 1998, while I was still a second-year undergrad at Sharif University, I sent him an email asking whether he was aware of any book similar to Garey & Johnson but for parallel computing (indeed this was my first remote interaction with him); I was shocked how fast he answered my email just in a couple of hours with a relevant reference. This was especially very exciting and encouraging for me, since several other people never answered my emails at that time. More interestingly, later in 2012, I told him personally that I admired him for answering that email. He told me just wait a second and in a couple of minutes, he could find the exact same email from 1998 that I sent him; then we even discussed some English improvements for the email text as well.

Second he was a perfectionist from several aspects. Here are some examples. He was often the reviewer for P=NP or P!=NP papers for several journals. Probably lots of us even do not look into these papers unless written by a well-known fellow; however he was reading these papers very carefully to find the exact bugs and mention them to the authors. Indeed even when I sent him several referee requests for conferences for which I severed as a PC member, he always spent a lot of time to read the paper very carefully and often came with novel improvements and simplifications, sometime in a extend that authors of the paper under review wanted to have this anonymous referee as a co-author. All these happened despite he was a very busy man; however he still considered the task of refereeing a paper very seriously and respected the authors (and I think this is an example that lots of us can learn from it). He was a very good writer as well and spent a lot of time to improve the presentation of a paper, simplify it, and present it in a perfect way. I am proud to have one paper coauthored with David, a very long paper with several co-authors. On this paper David had the lead and indeed spent all the years that I was with AT&T (and even after than) to prepare the journal version of the paper. Indeed he was sending us the almost final version on Dec 2014 (and asked us for comments) just a month before he was diagnosed with cancer (I hope that still we can send the paper to a journal given the time that David spent on it). Another example of his perfectionism: he attended ALL SODA while he was alive and almost ALL STOC and FOCS (expect 1-2 years that AT&T had travel restrictions). Not only that, anytime that there was any talk in the conference, he attended at least one session. Yet another example: we had group lunches every day at AT&T.  That was David’s habit to ask everyone in the group to see whether they want to join. Now the interesting point was that he came exactly at noon EVERY DAY and you could even set your watch for 12pm when you saw him for lunch.

He was founder of SODA, the best algorithms conference. Indeed lots of us know David because he was the founder of SODA and he was handling SODA business meetings for lots of year as the chair of the steering committee. As a result, I often had lots of discussion with him regarding SODA and its future. We discussed what the protocol for selecting the chair of SODA should be, whether SODA should have an official Rebuttal Phase or not, etc. During discussion even some interesting topics came up which are good to discuss in the community as well. David believed since SODAs (and in general other major TCS conferences) are the main venues for publications but still we need full and correct mathematical proofs for our claims (despite the rest of CS), we should have a five-year period that any major claims and theorems for which the authors do not provide full proofs in a verifiable manner in arxiv or in a journal during these five years should be considered officially open for everyone to grab, prove formally, and get the full credit for that. Another discussion was that ideally SODA (and again other major TCS conferences) should go double-blind like lots of other major CS conferences in other fields. This will help to have much more fair selection in which the name of authors do not give advantage/disadvantage for acceptance (though PC chair still could see the author lists for some extreme cases).

I can probably write pages and pages of other memories on David’s excellent personal characteristics (e.g. he was a marathon runner, he held the annual barbecue for AT&T/Bell-labs theory interns, researchers, and alumni for more than two decades,  he served in Army between his Masters and Ph.D. and kept the same types of spirits and disciplines in the rest of his life, he always emphasized on putting his middle initial “S.” in his name especially due to Airport Security since his name is a very common name, etc), but I think I should stop at this point.

I hope that we have a great memorial event for him in the next SODA (SODA’17) the conference that he founded.

Rest in Peace David,

From Mohammad

Complexity versus Complexity

For those interested, I've started writing posts for the Predictwise Blog. Predictwise makes predictions of future events such as who will win the Republican Nomination (currently Trump with an 80% probability) based on prediction markets and other betting sites. This has been a fascinating election in terms of predictions, strategies, rules and game theory and I'm happy to try and makes sense out of it over at Predictwise without subjecting my readers here at Computational Complexity with too many political posts.

A reader had asked me to comment on a Slate article The Theory of Everything and Then Some, a book review of John Miller's A Crude Look at the Whole: The Science of Complex Systems in Business, Life, and Society. John Miller is a social scientist who works on the other "complexity theory" that studies that "simple local rules can have complex global implications". Often complex systems work quite well, like the invisible hand of the economy, but sometimes things can go wrong and the article often mentions the "flash crash" of trading programs reacting to each other causing a major drop in stock prices in May of 2010.

Our fields with the similar names are not as different as might appear. Much of what they study are inherently computational-like processes and we also look at emergent behavior from simple operations of Turing machine; read, write and move the tape. What they call non-linear we call computation. We do take very different approaches. The computational complexity theory community proves theorems where we can and helps understand the mathematical challenges of when we can't. The other complexity theorists try to explain by examples, simulations and simplified models.

The two communities often, but not always, seem to have disdain for one another and that's a shame. The tools of computational complexity can help understand the power and limitations of complex systems. These collaborations require them to understand how we can help them and for us to be willing to work on problems that may not yield difficult-to-prove theorems. That's what attracts me to prediction markets, a very simple kind of information aggregation system that still is very difficult to analyze as a computational mechanism.

What's missing from the article is how tools like machine learning can play in helping to predict the outcomes of many complex systems. The big deluge of data that starts off the article may add to the complexity but it almost paradoxically also makes it possible to learn from it.

Hilary Putnam passed away on March 13

Hilary Putnam passed away on March 13, 2016. Some of the obits say he  was a philosopher, mathematician, logician, and computer scientist.

He is probably best known to readers of this blog for his work on Hilbert's 10 problem and resolution.

HILBERT  TENTH:

Recall H10 stated in current terminology: Find an ALGORITHM that will, given a poly p(x1,,...,,xn) in many variables, with coefficients in the integers, determine if it has a diophantine solution.

Martin Davis, Hilary  Putnam, and Julia Robinson showed that if you also allow exponentation then the problem is  undecidable in the early 1960s. Yuri Matijasevich in 1970 showed how to express exps in terms of polynomials to complete the proof. The solution to Hilbert's 10th problem is often credited to all four of them which seems right to me.

One consequence of there proof: for any c.e. set A there is a poly p such that

A = { x | exists x1,...,xn p(x,x1,...,xn)=0}

Later work got the polynomial down to 13 variables.



RESOLUTION:

John Robinson (but see comments)  and later papers by  Davis-Putnam aad later Davis-Logemann-Loveland devised resolution theorem proven which is an early SAT-solver algorithm. Many modern algorithms are based on it. (Note- earlier version of this post had mistakes in it. I thank Paul Beame's comments below for clarifying the history.)

HOW TO CLASSIFY HIM:

 I suspect that Hilary Putnam would call himself a philosopher since that was his MOTIVATION.  That may be the best way to classify people (if we are inclined to do that), don't look at WHAT they do look at WHY they do it.

PHIL OF MATH- one problem with Philosophy, even Phil of Math, is that its hard to have well defined questions and therefore hard to answer them. I am NOT criticizing the field, just saying why I would have a hard time working in it.

The Value of Shapley

Nobel laureate Lloyd Shapley passed away Saturday. We best know Shapley for his stable matching algorithm with David Gale. Nicole Immorlica guest posted on stable matching shortly after Gale's passing in 2008.

I'd like to talk about another great innovation, the Shapley Value, a solution concept for cooperative games. For example, suppose no candidate has a majority of candidates heading into the Republican convention and there is no winner on the first ballot. Now we have many delegates that might group themselves into coalitions, and a union of coalitions that have enough delegates can determine the nominee. Larger coalitions have more power than smaller ones but even a single delegate coalition could tip the election. The Shapley value gives weights to the coalitions that measures their relative power with some nice linear and symmetric properties. In this scenario, the Shapley value of a coalition is the probability that adding that coalition will tip the election when coalitions are added in a random order.

Game Theorist Robert Aumann, another Nobel laureate, used the Shapley value to predict winning coalitions in Israeli elections.

The main challenge of the Shapley value is computational, in general it is #P-complete to compute but it can be approximated efficiently.

On Phillip Rogaway's The Moral Character of Cryptographic Work.

Some people have emailed me asking me to blog about the paper The Moral Character of Cryptographic Work by Phillip Rogaway  I urge you to read it, even if you disagree with it. Especially if you disagree with it. (Hmm- how will you know if you don't read it!)

There are so many issues raised in this paper that it could be (and might be) the topic of many blog posts. The first three paragraphs are today's topic:

Preamble. Most academic cryptographers seem to think that our field is a fun, deep, and politically neutral game—a set of puzzles involving communicating parties and notional adversaries. This vision of who we are animates a field whose work is intellectually impressive and rapidly produced, but also quite inbred and divorced from real-world concerns. Is this what cryptography should be like? Is it how we should expend the bulk of our intellectual capital? 

For me, these questions came to a head with the Snowden disclosures of 2013. If cryptography’s most basic aim is to enable secure communications, how could it not be a colossal failure of our field when ordinary people lack even a modicum of communication privacy when interacting electronically? Yet I soon realized that most cryptographers didn’t see it this way. Most seemed to feel that the disclosures didn’t even implicate us cryptographers. 

I think that they do. So I want to talk about the moral obligations of cryptographers, and my community as a whole. This is not a topic cryptographers routinely discuss. In this post-Snowden era, I think it needs to be. 

My thoughts:

1) I would add that the Target Breaking, the SONY hack, and the OPM breakin might also show that crypto has been a failure. He doesn't seem to mention those but I think they strengthen his case.

2) Might it be Security that is a colossal failure? Of course, crypto and security go together so it may be hard to disentangle whose failure it is.

3) Might it be that good crypto research has been done but is not being used- the tech transfer problem. He later claims that this would be relevant if crypto worked on the right problems in the
first place.

4) I tend to think he's right. Rather than me telling you why I think he's right, just read his paper.

David Johnson (1945-2016)

David Johnson, a leader and advocate for algorithms and all of theoretical computer science, passed away yesterday at the age of 70. A truly sad day for us all.

David's 1979 book with Michael Garey, Computers and Intractability: A Guide to the Theory of NP-Completeness, is still the best reference on the topic and perhaps the single most important resource in any computer scientist's library. David Johnson also wrote the NP-completeness column for the Journal on Algorithms and later the ACM Transactions on Algorithms, as well as "A Catalog of Complexity Classes" for the 1990 Handbook of Theoretical Computer Science. David founded the Symposium on Discrete Algorithms (SODA), a conference that is now often mentioned with STOC and FOCS as a top theory venue. He created the DIMACS algorithms challenges. He led SIGACT from 1987-1991, really transforming that organization, and served as its face for many years thereafter. I'm only scratching the surface of what he's done for the community, and can think of no one who put more effort into making the theoretical computer science as strong as it is.

Of course David was a great researchers as well, working on NP-completeness and approximation algorithms.

He received an ACM Fellow in 1995, the first SIGACT Distinguished Service prize in 1997 and the Knuth Prize in 2010. He used his Knuth prize lecture to push for practical applications for our algorithms. Just last month he was elected into the National Academy of Engineering.

I worked with David Johnson closely on various SIGACT activities. David never missed a STOC and we always invited him to the SIGACT Executive Committee dinners, not because he had an official role, but because he was David Johnson. I truly respected and admired David and glad I could call him a friend. We'll miss him deeply. STOC and SODA just won't be the same without him.

When do we care about the constants?

I've been reading two books recently: Asymptopia by Joel Spencer (He turns 70 soon!  Workshop for it!. My nephew things that celebrating your bday with a workshop would be... odd) and   The Joy of Factoring by Simon Wagtaff. In terms of content they are on two different topics. In terms of practicality they are different: Asymptopia is clearly a pure math book (there is one chapter on algorithms, but the rest is really pure math) whereas The Joy of Factoring is very practical in that it focuses on real algorithms for the important (for crytography) practical problem of factoring. However, there is one thing the books had in common: They both often care about multiplicative constants.

Example from Asymptopia: They gave better and better lower bounds on Ramsey numbers:

(1) R(k)  ≥  (1+o(1))(k/e sqrt(2)) 2^k/2  roughly (1+o(1))(0.26)2^k/2

(2) R(k)  ≥  (1+o(1))(k/e) 2^k/2 roughly (1+o(1))(1+o(1))(0.37)^k/2

(3) R(k)  ≥  (1+o(1))(k/sqrt(2)) 2^k/2 roughly (1+o(1))(0.71)^k/2

(It may be hard to read so I will clarify- the o(1) is little-o, a term that goes to 0 as k gets large.)

The first lower bound uses the prob method and you the reader has prob seen it or could prob derive it yourself. Prob. The second lower bound uses prob and a  clever way of coloring and then tossing out some vertices. The third lower bound uses the Local Lovasz Lemma.

Note that for this problem Joel Spencer cared about the constant.

Example from The Joy of Factoring: Since many (but not all!) factoring algorithms do not have rigorously proven run times (Number Theory is Hard!) it's harder to give clean examples here. The book often refers to tricks to get constants down and the notion that constants matters permeates the book. Here is one rigorous example of caring about constants:

Fermat's difference-of-squares algorithm goes as follows: We want to factor N. Let x=floor(sqrt(N)). Test each of the following numbers for being a square and stop when you get a square: x²-N, (x+1)²-N, (x+2)² - N, etc. When you find an r such that (x+r)²-N=y²  then you have (x+r-y)(x+u+y)=N. Almost surely this is a nontrivial factorization of N. (This algorithm is worse than the trivial sqrt(N) algorithm in some cases; however, it has some of the ideas needed for more sophisticated algorithms including the Quadratic Sieve.) Of course, one might be looking for the right r a long time. How long:

Let a be the largest divisor of N that is ≤ \sqrt(N). Let k=a/sqrt(N). Then the search will take

1+ (1-k)²sqrt(N)/(2k)

Again note that there are no hidden multiplicative constants.

So when do we care about constants and why?

1) If you are working on an algorithm for a problem people really want to solve then you need the constants to be small.

2) If you can get good bounds on the exact constants then you should.

3) If you have a technique and try it out you might end up just improving the constant. Even so, you have showed that the technique has merit.

4) Improving the constant may show progress which will later lead to more important improvements.

5) Chicken and Egg:  Here is an example from Asymptopia where he didn't care about the constant: Fix ε. Given three points in the unit square what is the prob that their area will be ≤ ε ?   He showed its Θ(ε).This proof is very nice. Tracking the constants used in his proof looks tedious. In order to care about the constants perhaps we need an interesting proof about them. To look for a proof technique that applies to them perhaps we need to care in the first place. Chicken and Egg?

Changing This Ancient Art Into a Science

The ACM announced yesterday that they will award the 2015 Turing Award to Whitfield Diffie and Martin Hellman for contributions to modern cryptography. The Turing award is the highest honor in all of computing. John Markoff in the New York Times also has the story.

Diffie and Hellman are best known for public-key cryptography, the brilliant idea that one could communicate secretly with someone you haven't communicated previously. Without public-key cryptography there would be no e-commerce. Equally important Diffie and Hellman brought computational complexity to bare, moving cryptography into its modern age. I strongly recommend reading their 1976 gem New Directions in Cryptography (PDF) particularly the introduction and chapter 6 where Diffie and Hellman connect cryptography to computational complexity and the P v NP problem itself defined only five years earlier. Here's the first paragraph:

We stand today on the brink of a revolution in cryptography. The development of cheap digital hardware has freed it from the design limitations of mechanical computing and brought the cost of high grade cryptographic devices down to where they can be used in such commercial applications as remote key cash dispensers and computer terminals. In turn, such applications create a need for new types of cryptographic systems which minimize the necessity of secure key distribution channels and supply the equivalent of a written signature. At the same time, theoretical developments in information theory and computer science show promise of providing provably secure cryptosystems, changing this ancient art into a science. 

One question for which I shall offer no opinion: Should Ralph Merkle have been a co-recipient of this award? 

It works in practice, but does it work in theory (Pollard's Factorization algorithm)

Throughout this post I ignore  polylog factors.

It is trivial to factor N in time N^1/2.  Pollard's rho-algorithm (see my write up here or Wikipedia Entry) for factoring does bette expected time N^1/4. Or does it?  It works well in practice but  has not been proven to work well in theory. (If I missed some paper that DID prove it works well in theory please leave a polite comment.)

Here we state a conjectures that, if true, will show that  Pollard's algorithm is in time (randomized)  N^1/4.  Let p be a prime. Let c be in {2,...,p-1}.

Let f_c(x)= x² + c mod p.

x₁ will be specified in the conjecture. x_i is f(x_i-1).

For at least half of the elements x₁ in {2,...,p-1} and at least half of the elements c in {2,...,p-1} the sequence x₁, x₂,... will have a repeat within the first O(p^1/2) items.

This is thought to be true since it is thought that the sequence is random-enough so that the birthday paradox will  work. Still... no proof.

When reading some algorithms papers the interest is in getting an algorithm that you can PROVE the run time of.  By contrast, papers on factoring and discrete log and other things that are used to break crypto systems the interest is more in getting something that actually works. I have to learn to stop thinking ``but they haven't proven that!'' and start thinking ``Oh, yes, that would work''. And to be fair, for Pollard's algorithms and others (e.g., quad sieve, number field sieve, which do better in practice than Pollard for large enough numbers) there are REASONS to think they will work well. 

More generally, theoretical and applied work may need different mentalities.

Primary Game Theory

[Nominations open for the SIGACT Distinguished Service Prize. Deadline: April 1]

The US presidential primaries have not gone as expected as you can see from the crazy shifts in the prediction markets. This year besides the usual democratic/republican split, we have an establishment/non-establishment split in both parties. Back in my day outside candidates like Trump, Cruz and Sanders would have run as independents like Ross Perot and John Anderson.

Despite the split, the establishment candidates focus more on themselves than the establishment. Christie's attack on Rubio in New Hampshire may have handed Trump the election and it certainly didn't save Christie's campaign. Kasich should just drop out now if he cares about keeping the nomination for an establishment candidate--it's just not his year, though maybe he's playing some game theory of his own.

The democratic side does not offer such interesting game theory, since we have a two horse race. Mostly a one horse race because the delegate math doesn't work well for Sanders.

Let's look at the election from the point of view of a hypothetical Georgia voter voting on Super Tuesday next week. Such a voter can choose which primary to vote on in election day.

Clinton will easily win Georgia but as long as Bernie gets at least 15% of the vote (likely), delegates will be allocated proportionally. So a vote in the democratic primary could affect a delegate but less likely to to affect who will be the nominee than on the Republican side. Unless Bernie surprises in South Carolina, the hypothetical voter may opt to vote in the Republican primary instead.

The republican delegate allocation rules most likely mean that the candidates receiving at least 20% of the votes will get a proportional allocation of 31 delegates and the winner in each of the 14 congressional districts gets two delegates while the runner up gets one. Looking at the polls, Trump will easily win the election with Cruz and Rubio hovering about 20%. A single vote could affect 6 delegates (20% of Georgia's at large 31 delegates). A vote for Kasich or Carson would not net Kasich or Carson any delegates but could bolster Trump by pushing Rubio's vote percentage down towards that 20% mark.

This scenario plays out across the Super Tuesday primaries. Trump is favored to win in every state voting that day except Cruz's Texas. If Rubio can get at least 20% of the vote in those states he keeps the race alive and could make up ground in winner-take-all states coming up later. Kasich doesn't draw much voters but enough that by not dropping out he may help close out this election on Tuesday. Game theory indeed.

In an early primary season already full of surprises we may see many more. It would be a lot more fun to watch if the fate of the US and the entire world didn't depend on the outcome.

What is a `previous publication'?

 Here are the guidelines about submission to STOC 2015 with regard to
submitting a prior published paper. I assume that most of the Theory Conferences have a similar policy.


Prior and Simultaneous Submissions: The conference will follow SIGACT's policy  on prior publication and simultaneous submissions. Abstract material which has  been previously published in another conference proceedings or journal, or  which is scheduled for publication prior to July 2015, will not be considered  for acceptance at STOC 2015. The only exception to this policy are prior or  simultaneous publications appearing in the Science and Nature journals.  SIGACT policy does not allow simultaneous submissions of the same (or essentially the same) abstract material to another conference with  published proceedings. The program committee may consult with program chairs of other (past or future) conferences to find out about closely related  submissions.

Here is a question that I ask non-rhetorically. What if Alice has a paper in arXiv in 2010 and submits it to STOC in 2012. Technically it has not been published before. However, it certainly is not new.

Should this be allowed? Under the current rules of course YES. Should the rules be changed? A paper can be out there  without it being published. Should the rules be changed to reflect this? I think NOT since it might be hard to define carefully and I don't want people to discourage posting on arXiv.

Should the committee be allowed to take its not-newness into account in judging it?  Do they already?  And the notion of   well known or out there are subjective.

BOB: This paper has been known about for years.

EVE: Well, I didn't know about it, so for ME its new!

There might be a newness/quality trade off. If Donna posted her proof that P=NP in 2020 but submitted it to STOC 2030, I think it would still get in. By contrast if Bob posts a proof of a good but not great paper that is STOC-worthy in 2020, and then submits it in 2030,, I think it would not get in.

Then again, by 2030 maybe we will have changed the prestige-conference model we currently use.

Posting Papers

In the ancient days of the 80's, if someone wanted a paper from you, they would ask and you would mail via post. Sometimes I would get a self-addressed envelope asking for a certain paper. Departments would maintain collections of local technical reports. Someone could request a paper, an admin would make a copy, slap on a cover and send it out.

In the 90's, we started distributing papers by email, but then who you sent papers to started to matter. As soon as we had a browser in 1993, for fairness, though more because I got tired of responding to paper requests, I put together a page that had electronic copies of all my papers. Over the years those files have gone from postscript to pdf and the page started as html and later I used bib2html which I kept going on my old Chicago CS account that nobody bothered turning off. Bib2html failed to work for me last week, I asked the twitterverse for an alternative and they answered. I went with bibbase and now can reveal my new paper page. Pretty easy to tell from the page when I started as a department chair. I kept the old page active just in case but it will no longer be updated.

Sometimes I wonder why I bother and just let people use Google Scholar or DBLP to find my papers. I guess I'm just not ready to give up this record of my research life.

∑{p≤ n} 1/p = ln(ln(n)) + o(1). read it here because....

(Last April fools day I  posted four links to stories that seemed absurd and asked which one was false. They all were true. I recently came across five  stories that all seem absurd but are all real, but three of them can't wait until April 1 since they are about current political events. Here they are:
Amazon to open many brick-and-mortar stores.
Why John Kasich got second place in New Hampshire (whch was better than expected).
Jim Gilmore's (who?) low expectations,
Why Ben Carson left Iowa.
airpnp- not about P vs NP
Donald Trump defends.... (I added this one on March 14)
And now back to our regularly scheduled blog)




A while back Larry Washington (number theorist at UMCP) showed me a simple proof that

∑_{p ≤ n} 1/p = ln(ln(n)) + o(1)

(p goes through all the primes ≤ n.)

Recently I tried to remember it and could not so I looked on the web and... I could not find it! I found proofs that the sum is at least ln(ln(n)) as part of a proof that the series diverges, but could not find a simple  proof of the equality.

I asked Larry Washington to email me the proof, and then (and this happens often) while waiting for the response I came up with it.

Anyway, to try to avoid what Lance pondered, the deterioratation of math over time, I post the proof here.Read it here since you probably can't find this proof elsewhere.

I continue to be amazed at both what IS and IS NOT on the web.

(ADDED LATER- one of the comments pointed to links on the web that DO contain the proofs I could not find.)

Test of Time Award- a good idea but...

The ESA Conference (European Symposium on Algorithms) has a test-of-time award
which

recognizes outstanding papers in algorithms research that were published in the ESA proceedings 19-21 years ago and which are still influential and stimulating the field today.

This sounds like a great idea- some papers are more influential then people might have thought when they first got into ESA, and some papers are less influential then people might have thought. And I am happy that Samir Khuller (my chair) and Sudipto Guha (a grad student when the paper was written) won it for their paper Approximating Algorithms for Connected Dominating Sets.

But there are two things that are not quite right.

1) 19-21 years. That seems like a very small window.  '

2) The paper has to have been published in ESA.

Together this makes the job of the panel that decides the award easier as they only have to look at three years of conferences.  But there are many fine papers in algorithms that are not in ESA and there may be an awesome three year period and then a draught, so the window seems short.

But rather than complain let me ask some well defined questions:

Are there any other awards with a lower limit (in this case 19 years) on how long the paper has to be out, so that its influence can be better appreciated? This is a good idea, though 19 seems high.  Awards for a lifetime of work are often similar in that the are given after the works influence is known.

Are there any other awards that restrict themselves to ONE conference or journal? Of course best-paper and best-student-paper awards to that, but I don't know of any others.

ADDED LATER: A commenter says that there are LOTS of test-of-time awards associated to conferences:

see here

STOC, FOCS, SODA, CCC don't have them so I foolishly thought that was representative.
That raises another question - why do some conferences have it and some dont'?

The Moral Hazard of Avoiding Complexity Assumptions

Moshe Vardi's CACM editor letter The Moral Hazard of Complexity-Theoretic Assumptions practically begs a response from this blog. I also encourage you to read the discussion between Moshe and Piotr Indyk and a twitter discussion between Moshe and Ryan Williams.

I take issue mostly with the title of Vardi's letter. Unfortunately we don't have the tools to prove strong unconditional lower bounds on solving problems. In computational complexity we rely on hardness assumptions, like P ≠ NP, to show that various problems are difficult to solve. Some of these assumptions, like the strong exponential-time hypothesis, the Unique Games Conjecture, the circuits lower bounds needed for full derandomization, are quite strong and we can't be completely confident that these assumptions are true. Nevertheless computer scientists will not likely disprove these assumptions in the near future so they do point to the extreme hardness of solving problems like getting a better than quadratic upper bound for edit distance or a better than 2-ε approximation for vertex cover.

If you read Vardi's letter, he doesn't disagree with the above paragraph. His piece focuses instead on the press that oversells theory results, claiming the efficiency of Babai's new graph isomorphism algorithm or the impossibility of improving edit distance. A science writer friend once told me that scientists always want an article to be fully and technically correct, but he doesn't write for scientists, he writes for the readers who want to be excited by science. Scientists rarely mislead the press, and we shouldn't, but do we really want to force science writers to downplay the story? These stories might not be completely accurate but if we can get the public interested in theoretical computer science we all win. To paraphrase Oscar Wilde, as I tweeted, the only thing worse than the press talking about theoretical computer science results is the press not talking about theoretical computer science results.

Go Google Go

In 2009 I posted about a surprising new approach that moved computer Go from programs that lose to beginners to where it could beat good amateurs. That approach, now called Monte Carlo Tree Search, involves evaluating a position using random game play and doing a bounded-depth tree search to maximize the evaluation.

Google last week announced AlphaGo, a program that uses ML techniques to optimize MCTS. This program beat the European Go champion five games to none, a huge advance over beating amateurs. In March AlphaGo will play the world Go champion, Lee Sedol, in a five game match. The world will follow the match closely (on YouTube naturally). For now we should keep our expectations in check, Deep Blue failed to beat Kasparov in its first attempt.

Google researchers describe AlphaGo in detail in a readable Nature article. To oversimplify they train deep neural nets to learn two functions, the probability of a win from a given position, and the probability distribution used to choose the next move in the random game play in MCTS. First they train with supervised learning based on historical game data between expert players and then reinforcement learning by basically having the program play itself. AlphaGo uses these functions to guide the Monte Carlo Tree Search.

AlphaGo differs quite a bit from chess algorithms.

• AlphaGo uses no built-in strategy for Go. The same approach could be used for most other two player games. I guess this approach would fail miserably for Chess but I would love to see it tried.
• Machine learning has the nice property that you can train offline slowly and then apply the resulting neural nets quickly during gameplay. While we can refine the chess algorithms offline but all the computation generally happens during the game.
• If a computer chess program makes a surprising move, good or bad, one can work through the code and figure out why the program made that particular move. If AlphaGo makes a surprising move, we'll have no clue why.
• I wonder if the same applies to human play. A chess player can explain the reasoning behind a particular move. Can Go players do the same or do great Go players rely more on intuition?

Machine learning applications like AlphaGo seemingly tackle difficult computational problems with virtually no built-in domain knowledge. Except for generating the game data for the supervised learning, humans play little role in how AlphaGo decides what to do. ML uses the same techniques to translate languages, to weed out spam, to set the temperature in my house, and in the near future to drive my car. Will they prove our theorems? Time will tell. 

Math questions that come out of the Iowa Caucus

Link for info I refer to here

Jim Gilmore, republican, has 0% of the vote. Does that mean that literally NOBODY voted for him?

Hillary beat Bernie , but BOTH get 21 delegates. I hardly call that a win. I call that a tie.


Why do we refer to Hillary and Bernie by their first names, but most of the republicans by their last name. The only exception is Jeb! who we call Jeb to dist from his brother. Also, I think he wants to play down his relation to his brother. Not that it will matter.

Cruz/Trump/Rubio will get 8,7,6 delegates.(This might change but not by a lot). I'd call that a tie. Later states will be winner-take-all which make no sense in a race with this many people (though it may go down soon-- Huckabee has already suspended his campaign which seems like an odd way of saying I quit). But in winner-take-all states there will be real winners.  Why are there winner-take-all states? It was a deal made so that those states wouldn't move their primaries up.

This is a terrible way to pick a president. I don't mean democracy which is fine, I mean the confusing combination of Caucus's and Primaries, with some states winner-take-all, some by proportion, and Iowa and NH having... more power than they should.  This was NOT a planned system it just evolved that way. But its hard to change.

If you are a registered Republican  but want Hillary to win then do you (1) vote for the republican you like the best, or (2) vote for the Republican that Hillary can most easily beat. The problem with (2) is that you could end up with President Trump.

Stat analysis of polls and looking at past trends have their limits for two reasons:

1) The amount of data is small. The modern primary system has only been in place since 1972.  Some nominations are incumbents which are very different from a free-for-all. The only times both parties had free-for-alls were 1988, 2000, 2008, and 2016.

2) Whatever trends you do find, even if they are long term (e.g.,  the tallest candidate wins) might just change. The old Machine Learning warning: Trends hold until they don't.

Most sciences get BETTER over time. Polling is a mixed bag. On the one hand, using modern technology you can poll more people. On the other hand, people have so many diff ways to contact them that its hard to know what to do. For example, its no longer the case that everyone has a landline.

Is this headline a satire?:here


AI project- write a program that tells political satire from political fact. Might be hard.

My wife pointed out that

Hillary WINS since she didn't lose!

Bernie WINS since an insurgent who TIES the favorite is a win

Cruz WINS since... well, he actually DID win

Trump WINS since his support is mostly real and he didn't collapse. And he was surprisingly gracious in his concession speech. (This is the weakest `he WINS' argument on this list)

Rubio might be the BIG WINNER since he did way better than expected. Thats a rather odd criteria and it makes people want to set their expectations low.

SO--- like a little league game where they all tried hard, THE'RE ALL WINNERS!

 The American Public--- not so much.

We Still Can't Beat Relativization

As we celebrate our successes in computational complexity here's a sobering fact: We have had no new non-relativizing techniques in the last 25 years.

A little background: In 1975, a few years after Cook established the P v NP problem, Baker, Gill and Solovay created two sets A and B such that every NP machine that could ask questions about A could be simulated by a P machine that could ask questions to A and there is some language accepted by an NP machine that could ask questions to B that cannot be solved by a P machine that could ask questions to B. In other words P^A = NP^A but P^B ≠ NP^B.

All the known proof techniques at the time relativized, i.e., if you proved two classes were the same or different, they would be the same of different relative to any set. BGS implied that these techniques could not settle the P v NP problem.

In the 80's and 90's we got very good at creating these relativized worlds and, with a couple of exceptions, we created relativized worlds that make nearly all the open questions of complexity classes between P and PSPACE both true and false.

There were some results in the that were non-relativizing for technical uninteresting reasons. In the late 80s/early 90s we had some progress, results like NP having zero-knowledge proofs, co-NP (and later PSPACE) having interactive proofs and NEXP having (exponential-sized) probabilistically checkable proofs, despite relativized worlds making those statements false. But then it stopped. We had a few more nonrelativizing results but those just used the results above, not any new techniques.

In 1994 I wrote on survey on what relativization meant post-interactive proofs, still mostly up to date. We have seen new barriers put up such as natural proofs and algebrization, but until we can at least get past traditional relativization we just cannot make much more progress with complexity classes.

When do we stop giving the original reference?

I was preparing  a talk which included my result that there is a sane reduction 4-COL \le 3-COL (the paper is here) when I  realized that if I am going to claim the reduction is by Gasarch then I should find out and credit the person who proved 3-COL NP-complete (I assume that the result 3-COL \le 4-COL is too trivial to have an author).  I could not find the ref on the web (I am sure that one can find it on the web, but a cursory glance did not yield it).  The reference was not in Goldreich's complexity book, nor the CLR Algorithms book. I suspect its not in most recent books.

The reference is Stockmeyer, SIGACT NEWS 1973,

Few modern paper references Cook or Levin's original papers for the Cook-Levin Theorem. I've even heard thats a sign its a crank paper.

Few modern papers reference Ramsey's original paper for Ramsey's Theorem.

But the questions arises--- when is a result such common knowledge that a ref is no longer needed?

A result can also go through a phase where the reference is to a book that contains it, rather than the original paper.

On the one hand, one SHOULD ref the original so that people know who did it and what year it was from. On the other hand there has to be a limit to this or else we would all be refering to Euclid and Pythagoras.

Where does Stockmeyer's result fall? I do not know; however, I've noticed that I didn't reference him, and I will correct that.

The Growing Academic Divide

The decreases of the past three years bring the number of advertised jobs to a new low, below the level reached after the severe drop between 2007–08 and 2009–10. 

So reads the Report on the Modern Language Association Job Information List. The MLA is the main scholarly organization for the humanities in the US. The bright spot--we aren't Japan.

Meanwhile in computer science we continue to see large enrollment increases in major, minors and students just wanting to take computer science courses. In the upcoming CRA Snowbird Conference "a major focus of the conference will be booming enrollments, with a short plenary followed by parallel sessions devoted to the topic, its various ramifications, and ideas to help you deal with it, including best practices for managing growth."

The 2015 November CRA News had 83 pages of faculty job ads, up from 75 in 2014 and 34 in 2012. This doesn't even count that fact that many departments are looking to hire two, three, four or more positions in CS. It will be an interesting job market this spring.

All of this is driven by jobs. We can't produce enough strong computer scientists to fill industry demand. And it's becoming increasingly hard for a humanities major to get a good first job.

It's nice to be on the side of growth but it's a shame that faculty hiring seems to be a zero-sum game. We need poets as well as nerds. We've help create a world where we have made ourselves indispensable but is this a world we really want to live in?