Given strings and of characters each, the textbook dynamic programming algorithm finds their edit distance in time (if you haven’t seen this in your undergrad algorithms class, consider asking your university for a refund on your tuition). Recent complexity breakthroughs [1][2] show that under plausible assumptions like SETH, quadratic time is almost optimal for exact algorithms. This is too bad, because we like to compute edit distance between very long strings, like entire genomes of two organisms (see also this article in Quanta). There is a sequence of near-linear time algorithms with improved approximation factors [1][2][3][4], but until now the state of the art was polylogarithmic; actually for near-linear time, this is still the state of the art:

**Open question 1**: Is there a constant-factor approximation to edit distance that runs in near-linear time?

Here is a sketch of *an *algorithm. It is somewhat different from the algorithm in the paper because I wrote this post before finding the full paper online.

We partition each string into *windows*, or consecutive substrings of length each. We then restrict our attention to *window-compatible* matchings: that is, instead of looking for the globally optimum way to transform to , we look for a partial matching between the – and -windows, and transform each -window to its matching -windows (unmatched -windows are deleted, and unmatched -windows are inserted). It turns out that restricting to window-compatible matchings is almost without loss of generality.

In order to find the optimum window-compatible matching, we can find the distances between every pair of windows, and then use a (weighted) dynamic program of size . The reason I call it “Step 0” is because so far we made zero progress on running time: we still have to compute the edit distance between pairs, and each computation takes time , so time in total.

Approximating all the pairwise distances reduces to the following problem: given threshold , compute the bipartite graph over the windows, where two windows and share an edge if . In fact it suffices to compute an approximate , where and may share an edge even if their edit distance is a little more than .

**New Goal**: Compute faster than naively computing all pairwise edit distances.

While there are many edges in , say average degree : Draw a random edge , and let be two other neighbors of , respectively. Applying the **triangle inequality** (twice), we have that , so we can immediately add to . In expectation, have neighbors each, so we discovered a total of pairs; of which we expect that roughly correspond to *new* edges in . Repeat at most times until we discovered almost all the edges in . Notice that each iteration took us time (computing all the edit distances from and ); hence in total only . Thus we reduced to the sparse case in truly subquadratic time.

The algorithm up to this point is actually due to a recent paper by Boroujeni et al; for the case when is relatively sparse, they use Grover Search to discover all the remaining edges in quantum subquadratic time. It remains to see how to do it classically…

The main observation we need for this part is that if windows and are close, then in an optimum window-compatible matching they are probably not matched to -windows that are very far apart. And in the rare event that they are matched to far-apart -windows, the cost of inserting so many characters between and outweighs the cost of completely replacing if we had to. So once we have a candidate list of -windows that might match to, it is safe to only search for good matches for around each of those candidates. But when the graph is sparse, we have such a short list: the neighbors of !

We have to be a bit careful: for example, it is possible that is not matched to any of its neighbors in . But if we sample enough ‘s from some interval around , then either (i) at least one of them is matched to a neighbor in ; or (ii) doesn’t contribute much to reducing the edit distance for this interval, so it’s OK to miss some of those edges.

On the back of my virtual envelope, I think the above ideas give a -approximation. But as far as genomes go, up to a -approximation, you’re as closely related to your dog as to a banana. So it would be great to improve the approximation factor:

**Open question 2**: Is there a -approximation algorithm for edit distance in truly subquadratic (or near-linear) time?

Note that only the sparsification step loses more than in approximation. Also, none of the existing fine-grained hardness results rule out an -approximation, even in linear time!

]]>In the same vein, Michael Ekstrand and Michael Veale (the Publicity Chairs for FAT* 2019) have asked me to disseminate the following announcement and CFP.

———–

We are pleased to announce the Call for Papers for the 2019 ACM Conference on Fairness, Accountability, and Transparency (FAT*), to be held in Atlanta, Georgia in January/February 2019.

FAT* is an interdisciplinary conference to connect social, technical and policy domains around broad questions of fairness, accountability and transparency of machine learning, information retrieval, and other computing systems. The conference this year features tracks on Theory And Security, Statistics, Machine Learning, and Data Mining. The inaugural conference at NYU in February 2018 had an acceptance rate of 25% and was sold-out, with 450 international attendees from across academia, industry and public policy.

Papers (8-10 pages, due August 23) are double-blind peer reviewed and published in conference proceedings in the ACM Digital Library. Authors can also opt for non-archival submission, subject to the same review process but only appearing as an abstract in the proceedings. The theoretical computer science community has been involved in work on algorithmic fairness since its inception, and we hope that you’ll consider FAT* as a venue for your work.

Please forward this call to other people or groups you think may be interested.

For more details, see https://fatconference.org/2019/cfp.html

]]>1. For quantum communication, we lose a quadratic factor (corresponding to Grover’s search), i.e. our lower bound is only . But I don’t know how to use Grover’s search to improve over the naive upper bound. So, is the quantum communication of approximate Nash equilibrium closer to linear or quadratic?

Before we discuss why quantum communication of approximate Nash is interesting, it is helpful to first recall some game theory, and in particular remind ourselves why the classical (randomized) communication complexity of approximate Nash is important. Briefly, a two-player game is described by two matrices ; if Alice and Bob play actions , their payoffs are and , respectively. Typically, they want to use randomized strategies (called *mixed strategies*). We say that Alice and Bob are at an (approximate) Nash equilibrium, each player’s strategy is (approximately) best-response to other player’s strategy. I.e. once players are at an equilibrium, they may never want to leave it. The big question is how do they get there in the first place?

A common approach to this question is to look for plausible *dynamics*, or procedures by which players update their strategies, and which guarantee convergence to Nash equilibrium. Defining “plausible” is a fascinating philosophical discussion far beyond the scope of this post, but two useful desiderata are: (i) *uncoupled dynamics*, namely each player knows only her own payoff matrix and the history of the game — this rules out the trivial dynamics where players start at a Nash equilibrium; and (ii) *efficient dynamics*, namely the dynamics must converge faster than it would take Alice to communicate her entire payoff matrix to Bob. Those are certainly not sufficient conditions for plausibility of dynamics, but our communication lower bound rules out *any* efficient uncoupled dynamics.

So, what is a natural model of quantum uncoupled dynamics? I was confused about this for a few weeks: people have studied quantum games where players’ actions are described by qubits, and the payoffs are determined based on their measurements. But this is a generalization of classical games, where we already know that the problem is hard. So I asked Shalev again, and he had another nice observation: the players can still send classical bits (aka play classical actions) — they merely need to share entangled qubits and measure them before deciding what strategies to play. (But admittedly this might not work if the police decide to search the Dilemma Prisoners for entangled qubits before their interrogation…)

One last motivational comment: my very superficial understanding of the real-world feasibility of all this stuff is that while there is a lot of buzz around the race toward the first quantum *computer* that may or may not be able to execute a “hello world!” program [1][2][3], quantum *communication* already allows cross-continental video conferences…

While writing this post, I realized that there is an entire literature on various ways to entangle quantum with game theory. My favorite is this paper by Alan Deckelbaum about **quantum correlated equilibrium**. Correlated equilibrium is a generalization of Nash equilibrium where a trusted *coordinating device* suggests to Alice and Bob pairs of actions drawn from a joint (correlated) distribution. The requirement is that Alice, after seeing the action the coordinating device suggested for her (but not the one for Bob), has no incentive to deviate from the suggestion. It is known that natural no-internal-regret dynamics converge to the *set* of correlated equilibria. But without the trusted coordinating device the players are still incentivized to keep modifying their strategies. (By the way, the classical communication complexity of approximate correlated equilibrium in two-player games is still open!)

Anyway, Deckelbaum points out that any correlated distribution can be simulated using quantum entanglement. Can quantum entanglement replace the trusted coordinating device? Sometimes, but there is a catch: sampling from the correlated distribution using quantum measurements requires players to cooperate with the sampling protocol. Specifically, Deckelbaum shows that some games have correlated equilibria that cannot be truthfully sampled with quantum entanglement, i.e. one of the players has an incentive to deviate from any sampling protocol. He defines quantum correlated equilibria as those that can be sampled truthfully, and asks what is the computational complexity of finding one. (Note that this is an easier question than the PPAD-complete Nash equilibrium, and harder than the polynomial-time correlated equilibrium.) So here is yet another nice question:

2. What is the (randomized/quantum) communication complexity of finding an approximate quantum correlated equilibrium?

]]>Success in your career will be determined more by your weaknesses than

by your strengths. Thus, if you imagine plotting a sequence of scores

that rate your ability to carry out different kinds of tasks, it’s

far better to have a high minimum than a high maximum. Try to identify

your weaknesses and to overcome as many as you can.

Every large project has parts that are fun and parts that are dull.

Learn to get through the dull parts. Never postpone a

distasteful-but-necessary portion of work-to-be-done, unless

there’s a very good reason why you’ll be able to do it better later.

Niels Hendrik Abel gave wonderful advice: “Read the masters!”

Take the time to read lots of papers that were written by top researchers

when they were first discovering important ideas. Study the works of

great computer scientists, and do your best to understand their mindset.

In order to do this well, you’ll have to learn how to put yourself into

their place — remembering what they knew and didn’t know at the time,

and adjusting to their terminology and notation. The exercise of “getting

inside another person’s head” is, in itself, extremely valuable for

building your own mental skills.

Here’s a trick that I often use when reading a technical book or paper:

After the author has stated a problem to be solved (or a theorem to be

proved, etc.), I cover up the text and spend some time trying to solve

that problem by myself. Similarly, before turning the page, I try to

guess what’s on the next page. Of course I usually fail … but even

in failure, I’m much more ready to understand the author’s solution,

than if I hadn’t tried it first. Furthermore, with this modus operandi

I’m repeatedly learning new ways to get past stumbling blocks.

Instead of promoting yourself aggressively, you should try to write so

well that others can readily see for themselves the value of what you’ve

done. Then they’ll spontaneously also tell their friends, and the

word will spread. On the other hand, if a good writer comes to you and

wants to publish an account of your work, it never hurts to have a

good “press agent”.

PS. (from Don) re “reading the masters”

“The purpose of … reading is precisely to suspend one’s mind

in the workings of another sensibility”.

— Guy Davenport, quoted in Harvard Magazine Nov-Dec 2017, p54

———————————————————————————

I gender-transitioned two years ago, and Eurocrypt 2018 in Tel-Aviv is the first major conference I attend since then. I am a bit nervous. How much time does it take for 400 people to update my name and pronouns to use “Chris” and he/him? Two years feels like an eternity to me, but surely, some people will not have heard about my gender-transition. I will need to come out to some people.

Coming-out is very empowering, but after two years and uncountable coming-outs, I really wish that everyone knows that I am trans and gay.

A gay friend of mine remarks that when being bisexual/lesbian/gay, coming out is really never over, and one needs to come out again and again, to each new person. And really, he says, there is rarely a good time to bring it up.

“How come you didn’t know I am lesbian/gay?”, I heard from several friends, in shock, worried I might have wrongly assumed they are heterosexual.

How many LGBTQIA people are in our communities? I know some LGBTQIA people in the community, but how many more are there, and how can I find them?

This simple question leads to something which would become more important to me than I expected initially.

In the rump session, I give a coming-out talk, combined with an announcement for an LGBTQIA cryptographers meeting during the rump session break ( https://eurocrypt.2018.rump.cr.yp.to/4f756d069387ee90de62454a828a3b9b.pdf).

Giving this talk in itself was very nice. I enjoyed sharing my happiness with the community, see my happiness reflected in other people’s eyes. I enjoyed the many positive comments I received during the hours and days that followed, and the recognition of daring to be visible.

During the break, I am excited and nervous. How many people will come to the meeting? And who? More than 10 people come, most of which I knew without knowing they are LGBTQIA. We walk into the room, one by one, each with light in our eyes. We came out to each other, all of us, in that moment. It’s intimate, moving, exciting. Coming out remains deeply personal. It can be daunting, even in a warm, progressive environment such as our research community and even to an LGBTQIA subgroup.

After the rump session, we go to the gay-lesbian bar Shpagat in Tel-Aviv, in happy excitement. We are the last customers that night. The next day, during the breaks, we often find ourselves with a majority of LGBTQIA people in a conversation, we sit next to each other during talks. Something important happened.

In light of our increased visibility (to each other and to the community at large), there were more opportunities for coming outs the next days (or so was my impression, although I am only conscious of 2 explicit cases…). It was very liberating for me to share many of the following conference moments with LGBTQIA cryptographers who would add additional views to a heterosexual, cissexual perspective, and who would help me explain the sensitive issue of coming out to other caring members of our research community.

The research community is my permanent country of residence, my frame of reference, the source of almost all my long-term friendships – and enfin, in this country, there live quite a few LGBTQIA people, and the research community encourages us and shares our happiness.

We are going to organize more LGBTQIA meetings alongside cryptography-related conferences. I hope, there will be more such meetings inside and outside of CS. And we look forward to see the number of LGBTQIA researchers (that we are aware of) grow.

If you are an LGBTQIA researcher who wants to get in touch with us more discretely than at a public meeting (to talk to one of us, e.g., in the beginning of your PhD etc.), you can send an eMail to queercrypt@gmail.com. You can also use that eMail address to join our mailing list (for event announcements) and/or our WhatsApp group (include your phone number if you want to join the WhatsApp group). While the group centers around cryptography-related events, the group is not limited to researchers in cryptography.

]]>http://www.ics.uci.edu/~irani/safetoc.html

You wouldn’t be surprised if I say that the success of the committee is very important to our community. But they cannot do it alone. The committee encourages members of the community to contact any of the committee’s members with information or opinions. Lets make sure they know that we are with them and help them make our community better.

]]>Barna Saha, Sofya Raskhodnikova and Virgi Vassilevska Williams are organizing a women’s event to take place during STOC this year. It will include a women’s lunch, a panel of senior female researchers and more.

In addition, they have secured funding to provide travel scholarships for women to attend STOC, hopefully being able to bring junior graduate students who may not have a paper to the conference. The overall goal is to increase the interest and participation of women in TCS.

Here is the website for the event:

Here are the instructions for the TCS Women travel grant.

https://tcswomen.wordpress.com/tcs-women-travel-scholarship/

https://tcswomen.wordpress.com/tcs-women-travel-scholarship/

In this post, I would like to raise one of Phil’s 12 specific suggestions: “Figure out what research would frustrate the NSA. Then do it.” I have quite a bit of sympathy for this point of view. But in the world we live in, isn’t the view of government as “enemy number one” a bit outdated? How about the thousands of companies spying on us constantly and carelessly abusing our personal information? And what research would frustrate those privacy violators? Perhaps research on the most effective possible *governmental* regulations ?!? Oops …

Please let us know what you think.

Full disclosure: I have been employed by three big technology companies and have recently received research fellowship from a fourth (to study privacy). I was also, and still am, the recipient of governmental research grants. So I guess that so far my research is more pleasing than frustrating to both companies and governments.

]]>https://www.gopetition.com/petitions/a-pledge-for-inclusiveness-in-toc.html

Our main goal is to draw further attention of our community to the dangers of harassment in TOC and show support towards every member of our community who have been affected. If you feel comfortable with it, we would love it if you sign the pledge and please help us spread the word (on blogs, email lists or any other relevant forum).

Some comments:

- The pledge is meant as a personal commitment and we expect that each signer will interpret it in a personal manner.
- The phrasing of the pledge is the result of discussions with many of our TOC colleagues, but we hope that even if it doesn’t perfectly match your views, it comes close enough.
- This initiative doesn’t come instead of any additional action (of the sort discussed here) but is rather meant to encourage such activism.
- There are many reasons that colleagues who are fully supportive of the goals of this pledge may choose not to sign the pledge. Please don’t feel pressured to sign (as this would defeat the spirit of the pledge).
- Through discussions with legal experts who specialize in sexual harassment and related topics as well as with faculty members who handle sexual harassment in academia, we learned that the impact of such a pledge can be substantial (and that the exact phrasing is much less important).