Sometimes you see quantum popping up everywhere. I just did the opposite and gave a classical talk at a quantum workshop, part of an AMS meeting held at Northeastern University, which poured yet another avalanche of talks onto the Boston area. I spoke about the complexity of distributions, also featured in an earlier post, including a result I posted two weeks ago which gives a boolean function such that the output distribution of any AC circuit has statistical distance from for uniform . In particular, no AC circuit can compute much better than guessing at random *even if the circuit is allowed to sample the input itself. *The slides for the talk are here.

The new technique that enables this result I’ve called *entropy polarization*. Basically, for every AC circuit mapping any number of bits into bits, there exists a small set of restrictions such that:

(1) the restrictions preserve the output distribution, and

(2) for every restriction , the output distribution of the circuit restricted to either has min-entropy or . Whence *polarization*: the entropy will become either very small or very large.

Such a result is useless and trivial to prove with ; the critical feature is that one can obtain a much smaller of size .

Entropy polarization can be used in conjunction with a previous technique of mine that works for high min-entropy distributions to obtain the said sampling lower bound.

It would be interesting to see if any of this machinery can yield a separation between quantum and classical sampling for constant-depth circuits, which is probably a reason why I was invited to give this talk.

**Authors: **Barbara Geissmann, Stefano Leucci, Chih-Hung Liu, Paolo Penna **Download:** PDF**Abstract: **We consider the problem of sorting $n$ elements in the case of
\emph{persistent} comparison errors. In this model (Braverman and Mossel,
SODA'08), each comparison between two elements can be wrong with some fixed
(small) probability $p$, and \emph{comparisons cannot be repeated}. Sorting
perfectly in this model is impossible, and the objective is to minimize the
\emph{dislocation} of each element in the output sequence, that is, the
difference between its true rank and its position. Existing lower bounds for
this problem show that no algorithm can guarantee, with high probability,
\emph{maximum dislocation} and \emph{total dislocation} better than
$\Omega(\log n)$ and $\Omega(n)$, respectively, regardless of its running time.

In this paper, we present the first \emph{$O(n\log n)$-time} sorting algorithm that guarantees both \emph{$O(\log n)$ maximum dislocation} and \emph{$O(n)$ total dislocation} with high probability. Besides improving over the previous state-of-the art algorithms -- the best known algorithm had running time $\tilde{O}(n^{3/2})$ -- our result indicates that comparison errors do not make the problem computationally more difficult: a sequence with the best possible dislocation can be obtained in $O(n\log n)$ time and, even without comparison errors, $\Omega(n\log n)$ time is necessary to guarantee such dislocation bounds.

In order to achieve this optimal result, we solve two sub-problems, and the respective methods have their own merits for further application. One is how to locate a position in which to insert an element in an almost-sorted sequence having $O(\log n)$ maximum dislocation in such a way that the dislocation of the resulting sequence will still be $O(\log n)$. The other is how to simultaneously insert $m$ elements into an almost sorted sequence of $m$ different elements, such that the resulting sequence of $2m$ elements remains almost sorted.

**Authors: **Moritz Beck, Johannes Blum, Myroslav Kryven, Andre Löffler, Johannes Zink **Download:** PDF**Abstract: **Many applications in graph theory are motivated by routing or flow problems.
Among these problems is Steiner Orientation: given a mixed graph G (having
directed and undirected edges) and a set T of k terminal pairs in G, is there
an orientation of the undirected edges in G such that there is a directed path
for every terminal pair in T ? This problem was shown to be NP -complete by
Arkin and Hassin [1] and later W [1]-hard by Pilipczuk and Wahlstr\"om [7],
parametrized by k. On the other hand, there is an XP algorithm by Cygan et al.
[3] and a polynomial time algorithm for graphs without directed edges by Hassin
and Megiddo [5]. Chitnis and Feldmann [2] showed W [1]-hardness of the problem
for graphs of genus 1. We consider a further restriction to planar graphs and
show NP -completeness.

**Authors: **Zhiyi Huang, Zhihao Gavin Tang, Xiaowei Wu, Yuhao Zhang **Download:** PDF**Abstract: **We introduce a weighted version of the ranking algorithm by Karp et al. (STOC
1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online
bipartite matching problem when online vertices arrive in random order. Our
result shows that random arrivals help beating the 1-1/e barrier even in the
vertex-weighted case. We build on the randomized primal-dual framework by
Devanur et al. (SODA 2013) and design a two dimensional gain sharing function,
which depends not only on the rank of the offline vertex, but also on the
arrival time of the online vertex. To our knowledge, this is the first
competitive ratio strictly larger than 1-1/e for an online bipartite matching
problem achieved under the randomized primal-dual framework. Our algorithm has
a natural interpretation that offline vertices offer a larger portion of their
weights to the online vertices as time goes by, and each online vertex matches
the neighbor with the highest offer at its arrival.

**Authors: **Arnold Filtser, Ofer Neiman **Download:** PDF**Abstract: **Spanners for low dimensional spaces (e.g. Euclidean space of constant
dimension, or doubling metrics) are well understood. This lies in contrast to
the situation in high dimensional spaces, where except for the work of
Har-Peled, Indyk and Sidiropoulos (SODA 2013), who showed that any $n$-point
Euclidean metric has an $O(t)$-spanner with $\tilde{O}(n^{1+1/t^2})$ edges,
little is known.

In this paper we study several aspects of spanners in high dimensional normed spaces. First, we build spanners for finite subsets of $\ell_p$ with $1<p\le 2$. Second, our construction yields a spanner which is both sparse and also {\em light}, i.e., its total weight is not much larger than that of the minimum spanning tree. In particular, we show that any $n$-point subset of $\ell_p$ for $1<p\le 2$ has an $O(t)$-spanner with $n^{1+\tilde{O}(1/t^p)}$ edges and lightness $n^{\tilde{O}(1/t^p)}$.

In fact, our results are more general, and they apply to any metric space admitting a certain low diameter stochastic decomposition. It is known that arbitrary metric spaces have an $O(t)$-spanner with lightness $O(n^{1/t})$. We exhibit the following tradeoff: metrics with decomposability parameter $\nu=\nu(t)$ admit an $O(t)$-spanner with lightness $\tilde{O}(\nu^{1/t})$. For example, $n$-point Euclidean metrics have $\nu\le n^{1/t}$, metrics with doubling constant $\lambda$ have $\nu\le\lambda$, and graphs of genus $g$ have $\nu\le g$. While these families do admit a ($1+\epsilon$)-spanner, its lightness depend exponentially on the dimension (resp. $\log g$). Our construction alleviates this exponential dependency, at the cost of incurring larger stretch.

The TCS Group at KTH invites applications for a PhD position in CS focusing on algorithms for solving the Boolean satisfiability problem (SAT) very efficiently for large classes of instances, and on analyzing and understanding such algorithms. See http://www.csc.kth.se/~jakobn/openings/J-2018-0940-Eng.php for more information. Informal enquiries are welcome and may be sent to jakobn@kth.se .

Website: http://www.csc.kth.se/~jakobn/openings/J-2018-0940-Eng.php

Email: jakobn@kth.se

Sometimes a single word or phrase is enough to expand your mental toolkit across almost every subject. “Averaging argument.” “Motte and bailey.” “Empirically indistinguishable.” “Overfitting.” Yesterday I learned another such phrase: “Summer of the Shark.”

This, apparently, was the summer of 2001, when lacking more exciting news, the media gave massive coverage to every single shark attack it could find, creating the widespread impression of an epidemic—albeit, one that everyone forgot about after 9/11. In reality, depending on what you compare it to, the rate of shark attacks was either normal or unusually *low* in the summer of 2001. As far as I can tell, the situation is that the absolute number of shark attacks *has* been increasing over the decades, but the increase is *entirely* attributable to human population growth (and to way more surfers and scuba divers). The risk per person, always minuscule (cows apparently kill five times more people), appears to have been going down. This might or might not be related to the fact that shark populations are precipitously declining all over the world, due mostly to overfishing and finning, but also the destruction of habitat.

There’s a tendency—I notice it in myself—to say, “fine, news outlets have overhyped this trend; that’s what they do. But still, there must be *something* going on, since otherwise you wouldn’t see everyone talking about it.”

The point of the phrase “Summer of the Shark” is to remind yourself that a “trend” can be, and often is, **entirely** a product of people energetically looking for a certain thing, even while the actual rate of the thing is unremarkable, abnormally low, or declining. Of course this has been a favorite theme of Steven Pinker, but I don’t know if even reading his recent books, *Better Angels* and *Enlightenment Now*, fully brought home the problem’s pervasiveness for me. If a self-sustaining hype bubble can form even over something as relatively easy to measure as the number of shark attacks, imagine how common it must be with more nebulous social phenomena.

Without passing judgment—I’m unsure about many of them myself—how many of the following have you figured, based on the news or your Facebook or Twitter feeds, are probably some sort of epidemic?

- Crime by illegal immigrants
- Fraudulent voting by non-citizens
- SJWs silencing free speech on campus
- Unemployment in heartland America
- Outrageous treatment of customers by airlines
- Mass school shootings
- Sexism in Silicon Valley
- Racism at Starbucks

Now be honest: for how many of these do you have *any real idea* whether the problem is anomalously frequent relative to its historical rate, or to the analogous problems in other sectors of society? How many *seem* to be epidemics that require special explanations (“the dysfunctional culture of X”), but only because millions of people started worrying about these particular problems and discussing them—in many cases, thankfully so? How many seem to be epidemics, but only because people can now record outrageous instances with their smartphones, then make them viral on social media?

Needless to say, the discovery that a problem is *no worse* in domain X than it is in Y, or is better, doesn’t mean we shouldn’t fight hard to solve it in X—especially if X happens to be our business. Set thy own house in order. But it does mean that, if we see X but not Y attacked for its deeply entrenched, screwed-up culture, a culture that lets these things happen *over and over*, then we’re seeing a mistake at best, and the workings of prejudice at worst.

I’m not saying anything the slightest bit original here. But my personal interest is less in the “Summer of the Shark” phenomenon itself than in its *psychology*. Somehow, we need to figure out a trick to move this cognitive error from the periphery of consciousness to center stage. I mustn’t treat it as just a 10% correction: something to acknowledge intellectually, before I go on to share a rage-inducing headline on Facebook anyway, once I’ve hit on a suitable reason why my initial feelings of anger were basically justified after all. Sometimes it’s a 100% correction. I’ve been guilty, I’m sure, of helping to spread SotS-type narratives. And I’ve laughed when SotS narratives were uncritically wielded by others, for example in *The Onion*. I should do better.

I can’t resist sharing one of history’s most famous Jewish jokes, with apologies to those who know it. In the shtetl, a horrible rumor spreads: a Jewish man raped and murdered a beautiful little Christian girl in the forest. Terrified, the Jews gather in the synagogue and debate what to do. They know that the Cossacks won’t ask: “OK, but before we do anything rash, what’s the *rate* of Jewish perpetration of this sort of crime? How does it compare to the Gentile rate, after normalizing by the populations’ sizes? Also, what about Jewish victims of Gentile crimes? Is the presence of Jews causally related to more of our children being murdered than would otherwise be?” Instead, a mob will simply slaughter every Jew it can find. But then, just when it seems all is lost, the rabbi runs into the synagogue and jubilantly declares: “wonderful news, everyone! It turns out the murdered girl was Jewish!”

And now I should end this post, before it jumps the shark.

**Update:** This post by Scott Alexander, which I’d somehow forgotten about, makes exactly the same point, but better and more memorably. Oh well, one could do worse than to serve as a Cliff Notes and link farm for Slate Star Codex.

**Authors: **Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani **Download:** PDF**Abstract: **Graph Drawing Beyond Planarity is a rapidly growing research area that
classifies and studies geometric representations of non-planar graphs in terms
of forbidden crossing configurations. Aim of this survey is to describe the
main research directions in this area, the most prominent known results, and
some of the most challenging open problems.

**Authors: **Ahmad Biniaz, Prosenjit Bose, Aurélien Ooms, Sander Verdonschot **Download:** PDF**Abstract: **An "edge guard set" of a plane graph $G$ is a subset $\Gamma$ of edges of $G$
such that each face of $G$ is incident to an endpoint of an edge in $\Gamma$.
Such a set is said to guard $G$. We improve the known upper bounds on the
number of edges required to guard any $n$-vertex embedded planar graph $G$:

1- We present a simple inductive proof for a theorem of Everett and Rivera-Campo (1997) that $G$ can be guarded with at most $ \frac{2n}{5}$ edges, then extend this approach with a deeper analysis to yield an improved bound of $\frac{3n}{8}$ edges for any plane graph.

2- We prove that there exists an edge guard set of $G$ with at most $\frac{n}{3}+\frac{\alpha}{9}$ edges, where $\alpha$ is the number of quadrilateral faces in $G$. This improves the previous bound of $\frac{n}{3} + \alpha$ by Bose, Kirkpatrick, and Li (2003). Moreover, if there is no short path between any two quadrilateral faces in $G$, we show that $\frac{n}{3}$ edges suffice, removing the dependence on $\alpha$.

**Authors: **Markus Chimani, Ivo Hedtke, Tilo Wiedera **Download:** PDF**Abstract: **Given a graph $G$, the NP-hard Maximum Planar Subgraph problem asks for a
planar subgraph of $G$ with the maximum number of edges. The only known
non-trivial exact algorithm utilizes Kuratowski's famous planarity criterion
and can be formulated as an integer linear program (ILP) or a pseudo-boolean
satisfiability problem (PBS). We examine three alternative characterizations of
planarity regarding their applicability to model maximum planar subgraphs. For
each, we consider both ILP and PBS variants, investigate diverse formulation
aspects, and evaluate their practical performance.

**Authors: **Kun He, Qian Li, Xiaoming Sun, Jiapeng Zhang **Download:** PDF**Abstract: **Lov{\'a}sz Local Lemma (LLL) is a very powerful tool in combinatorics and
probability theory to show the possibility of avoiding all "bad" events under
some "weakly dependent" condition. Over the last decades, the algorithmic
aspect of LLL has also attracted lots of attention in theoretical computer
science. A tight criterion under which the abstract version LLL holds was given
by Shearer [shearer1985problem]. It turns out that Shearer's bound is generally
not tight for variable version LLL (VLLL) [he2017variable]. Recently, Ambainis
et al. introduced a quantum version LLL (QLLL), which was then shown to be
powerful for quantum satisfiability problem.

In this paper, we prove that Shearer's bound is tight for QLLL, affirming a conjecture proposed by Sattath et. al. Our result shows the tightness of Gily{\'e}n and Sattath's algorithm, and implies that the lattice gas partition function fully characterizes quantum satisfiability for almost all Hamiltonians with large enough qudits.

Commuting LLL (CLLL), LLL for commuting local Hamiltonians which are widely studied in literature, is also investigated here. We prove that the tight regions of CLLL and QLLL are generally different. Thus, the efficient region of algorithms for CLLL can go beyond shearer's bound. Our proof is by first bridging CLLL and VLLL on a family of interaction bipartite graphs and then applying the tools of VLLL, e.g., the gapless/gapful results, to CLLL. We also provide a sufficient and necessary condition for deciding whether the tight regions of QLLL and CLLL are the same for a given interaction bipartite graph.

**Authors: **Krishnendu Chatterjee, Wolfgang Dvořák, Monika Henzinger, Alexander Svozil **Download:** PDF**Abstract: **We consider planning problems for graphs, Markov decision processes (MDPs),
and games on graphs. While graphs represent the most basic planning model, MDPs
represent interaction with nature and games on graphs represent interaction
with an adversarial environment. We consider two planning problems where there
are k different target sets, and the problems are as follows: (a) the coverage
problem asks whether there is a plan for each individual target set, and (b)
the sequential target reachability problem asks whether the targets can be
reached in sequence. For the coverage problem, we present a linear-time
algorithm for graphs and quadratic conditional lower bound for MDPs and games
on graphs. For the sequential target problem, we present a linear-time
algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic
conditional lower bound for games on graphs. Our results with conditional lower
bounds establish (i) model-separation results showing that for the coverage
problem MDPs and games on graphs are harder than graphs and for the sequential
reachability problem games on graphs are harder than MDPs and graphs; (ii)
objective-separation results showing that for MDPs the coverage problem is
harder than the sequential target problem.

**Authors: **Aruni Choudhary, Arijit Ghosh **Download:** PDF**Abstract: **Delaunay protection is a measure of how far a Delaunay triangulation is from
being degenerate. In this short paper we study the protection properties and
other quality measures of the Delaunay triangulations of a family of lattices
that is obtained by distorting the integer grid in $\mathbb{R}^d$. We show that
the quality measures of this family are maximized for a certain distortion
parameter, and that for this parameter, the lattice is isometric to the
permutahedral lattice, which is a well-known object in discrete geometry.

**Authors: **Alastair Murray, Stuart Marshall, Leroy Cronin **Download:** PDF**Abstract: **How do we estimate the probability of an abundant objects' formation, with
minimal context or assumption about is origin? To explore this we have
previously introduced the concept of pathway assembly (as pathway complexity),
in a graph based context, as an approach to quantify the number of steps
required to assembly an object based on a hypothetical history of an objects
formation. By partitioning an object into its irreducible parts and counting
the steps by which the object can be reassembled from those parts, and
considering the probabilities of such steps, the probability that an abundance
of identical such objects could form in the absence of biological or
technologically driven processes can be estimated. Here we give a general
definition of pathway assembly from first principles to cover a wide range of
case, and explore some of these cases and applications which exemplify the
unique features of this approach.

**Authors: **Jayadev Acharya, Clément L. Canonne, Himanshu Tyagi **Download:** PDF**Abstract: **Independent samples from an unknown probability distribution $\mathbf{p}$ on
a domain of size $k$ are distributed across $n$ players, with each player
holding one sample. Each player can communicate $\ell$ bits to a central
referee in a simultaneous message passing (SMP) model of communication to help
the referee infer a property of the unknown $\mathbf{p}$. When $\ell\geq\log k$
bits, the problem reduces to the well-studied collocated case where all the
samples are available in one place. In this work, we focus on the
communication-starved setting of $\ell < \log k$, in which the landscape may
change drastically. We propose a general formulation for inference problems in
this distributed setting, and instantiate it to two prototypical inference
questions: learning and uniformity testing.

**Authors: **Lijie Chen, Erik D. Demaine, Yuzhou Gu, Virginia Vassilevska Williams, Yinzhan Xu, Yuancheng Yu **Download:** PDF**Abstract: **Since the introduction of retroactive data structures at SODA 2004, a major
unsolved problem has been to bound the gap between the best partially
retroactive data structure (where changes can be made to the past, but only the
present can be queried) and the best fully retroactive data structure (where
the past can also be queried) for any problem. It was proved in 2004 that any
partially retroactive data structure with operation time $T(n,m)$ can be
transformed into a fully retroactive data structure with operation time
$O(\sqrt{m} \cdot T(n,m))$, where $n$ is the size of the data structure and $m$
is the number of operations in the timeline [Demaine 2004], but it has been
open for 14 years whether such a gap is necessary.

In this paper, we prove nearly matching upper and lower bounds on this gap for all $n$ and $m$. We improve the upper bound for $n \ll \sqrt m$ by showing a new transformation with multiplicative overhead $n \log m$. We then prove a lower bound of $\min\{n \log m, \sqrt m\}^{1-o(1)}$ assuming any of the following conjectures:

- Conjecture I: Circuit SAT requires $2^{n - o(n)}$ time on $n$-input circuits of size $2^{o(n)}$. (Far weaker than the well-believed SETH conjecture, which asserts that CNF SAT with $n$ variables and $O(n)$ clauses already requires $2^{n-o(n)}$ time.)

- Conjecture II: Online $(\min,+)$ product between an integer $n\times n$ matrix and $n$ vectors requires $n^{3 - o(1)}$ time.

- Conjecture III (3-SUM Conjecture): Given three sets $A,B,C$ of integers, each of size $n$, deciding whether there exist $a \in A, b \in B, c \in C$ such that $a + b + c = 0$ requires $n^{2 - o(1)}$ time.

Our lower bound construction illustrates an interesting power of fully retroactive queries: they can be used to quickly solve batched pair evaluation. We believe this technique can prove useful for other data structure lower bounds, especially dynamic ones.

August 13-17, 2018 Saarbrücken, Germany http://resources.mpi-inf.mpg.de/conferences/adfocs/ ADFOCS is an international summer school with the purpose of introducing young researchers to topics which are the focus of current research in theoretical computer science. This year’s topic is *Fine-Grained Complexity and Algorithms*. The lecturers are Amir Abboud (IBM Almaden), Danupon Nanongkai (KTH), and Ramamohan Paturi (UC San … Continue reading 19th Max-Planck Advanced Course on the Foundations of Computer Science

A postdoc position on the complexity of CSPs is available at Oxford, supported by Standa Zivny’s ERC grant. The goal of the project is to study tractability (in a broad sense) of CSPs and convex relaxations. An ideal candidate would have a strong background in universal algebra and/or approximation algorithms/relaxations.

Website: http://www.cs.ox.ac.uk/news/1505-full.html

Email: standa.zivny@cs.ox.ac.uk

The next TCS+ talk will take place this coming Wednesday, April 25th at 1:00 PM Eastern Time (10:00 AM Pacific Time, 19:00 Central European Time, 18:00 UTC). **Danupon Nanongkai **from KTH will speak about “*Distributed All-Pairs Shortest Paths, Exactly*” (abstract below).

Please make sure you reserve a spot for your group to join us live by signing up on the online form. As usual, for more information about the TCS+ online seminar series and the upcoming talks, or to suggest a possible topic or speaker, please see the website.

Abstract: I will present the ~O(n^{5/4})-time distributed algorithm for computing all-pairs shortest paths exactly by Huang, Nanongkai, and Saranurak (FOCS 2017; https://arxiv.org/abs/1708.03903). The algorithm is fairly simple, and the talk will cover necessary backgrounds. I will also briefly survey recent progresses and some open problems in the field of distributed graph algorithms, where this work lies in.

As promised, an ad-hoc committee of theoretical computer scientists has been formed to combat harassment and discrimination. Here is the committee's charter:

"We are setting an ad-hoc committee to draft a proposal for joint ToC measures to combat discrimination, harassment, bullying, and retaliation, and all matters of ethics that might relate to that. Proposed measures may include, but are not restricted to, coordinating policies and guidelines, and setting community-wide institutions for reporting and oversight. The primary goal should be a determination to deter and root out such behavior in the theory community. The issues of false reporting and due process should be taken into account. The committee is expected to conduct the necessary research on existing practices. The committee will submit a report to the appointing organizations by September 30, 2018."

Members of the theory community (as broadly defined as you like) are **strongly** encouraged to contact any of the committee members with your input.

- Avrim Blum
- Erin Chambers
- Martin Farach-Colton
- Michal Feldman
- Sandy Irani (
*chair*) - Rafail Ostrovsky
- Pino Persiano
- Paul Spirakis

On June 26, as part of the STOC 2018 Theory Fest, Sofya Rashondnikova, Barna Saha, and Virginia Vassilevska Williams are organizing an inaugural meeting of TCS Women, a new community for female researchers in theoretical computer science and related areas, aimed at providing networking and mentoring opportunities, and to help combat discrimination and make the theory community more welcoming to everyone.

The inaugural meeting will include a panel of distinguished theory researchers (with confirmed participants Nina Mishra, Ronitt Rubinfeld, and Virgnia Vassilevska Williams), a women's lunch, and a research rump session.

Travel scholarships are available for junior women researchers to attend STOC, thanks to generous support from Google, Microsoft, and NSF. The application deadline is May 10.

For the first time in its 50 year history, STOC is offering subsidized child care for registered participants, at the rate of $40 per day for regular attendees and $25 per day for students. Please contact the local organizers Ilias Diakonikolas and David Kempe at stoc18childcare@gmail.com by June 11, two weeks before the start of the conference.

Yuval Rabani announced here the formation of an ad-hoc committee on sexual harassment. The committee is up, with a promising set of members, a very important charge and a deadline. Please look at the web page:

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.

We are pleased to announce that we will provide pooled, subsidized child care at STOC 2018. The cost will be $40 per day per child for regular conference attendees, and $20 per day per child for students. For more detailed information, including how to register for STOC 2018 childcare, see

http://acm-stoc.org/stoc2018/childcare.html

Ilias Diakonikolas and David Kempe (local arrangements chairs)

The organizers asked me to advertise this and I sympathize:

We are pleased to announce that we will provide pooled, subsidizedchild care at STOC 2018. The cost will be $40 per day per child forregular conference attendees, and $20 per day per child for students.

For more detailed information, including how to register for STOC 2018childcare, see http://acm-stoc.org/stoc2018/childcare.html

Ilias Diakonikolas and David Kempe (local arrangements chairs)

*(Announcement from Ilias Diakonikolas and David Kempe)*

We are pleased to announce that we will provide pooled, subsidized

child care at STOC 2018. The cost will be $40 per day per child for

regular conference attendees, and $20 per day per child for students.

For more detailed information, including how to register for STOC 2018

childcare, see http://acm-stoc.org/stoc2018/childcare.html

Ilias Diakonikolas and David Kempe (local arrangements chairs)

**Authors: **Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha **Download:** PDF**Abstract: **Random geometric graphs are the simplest, and perhaps the earliest possible
random graph model of spatial networks, introduced by Gilbert in 1961. In the
most basic setting, a random geometric graph $G(n,r)$ has $n$ vertices. Each
vertex of the graph is assigned a real number in $[0,1]$ randomly and
uniformly. There is an edge between two vertices if the corresponding two
random numbers differ by at most $r$ (to mitigate the boundary effect, let us
consider the Lee distance here, $d_L(u,v) = \min\{|u-v|, 1-|u-v|\}$). It is
well-known that the connectivity threshold regime for random geometric graphs
is at $r \approx \frac{\log n}{n}$. In particular, if $r = \frac{a\log n}{n}$,
then a random geometric graph is connected with high probability if and only if
$a > 1$. Consider $G(n,\frac{(1+\epsilon)\log{n}}{n})$ for any $\epsilon >0$ to
satisfy the connectivity requirement and delete half of its edges which have
distance at most $\frac{\log{n}}{2n}$. It is natural to believe that the
resultant graph will be disconnected. Surprisingly, we show that the graph
still remains connected!

Formally, generalizing random geometric graphs, we define a random annulus graph $G(n, [r_1, r_2]), r_1 <r_2$ with $n$ vertices. Each vertex of the graph is assigned a real number in $[0,1]$ randomly and uniformly as before. There is an edge between two vertices if the Lee distance between the corresponding two random numbers is between $r_1$ and $r_2$, $0<r_1<r_2$. Let us assume $r_1 = \frac{b \log n}{n},$ and $r_2 = \frac{a \log n}{n}, 0 <b <a$. We show that this graph is connected with high probability if and only if $a -b > \frac12$ and $a >1$. That is $G(n, [0,\frac{0.99\log n}{n}])$ is not connected but $G(n,[\frac{0.50 \log n}{n},\frac{1+\epsilon \log n}{n}])$ is.

This result is then used to give improved lower and upper bounds on the recovery threshold of the geometric block model.

**Authors: **Miriam Backens, Andrei Bulatov, Leslie Ann Goldberg, Colin McQuillan, Stanislav Živný **Download:** PDF**Abstract: **We analyse the complexity of approximate counting constraint satisfactions
problems $\mathrm{\#CSP}(\mathcal{F})$, where $\mathcal{F}$ is a set of
nonnegative rational-valued functions of Boolean variables. A complete
classification is known in the conservative case, where $\mathcal{F}$ is
assumed to contain arbitrary unary functions. We strengthen this result by
fixing any permissive strictly increasing unary function and any permissive
strictly decreasing unary function, and adding only those to $\mathcal{F}$:
this is weak conservativity. The resulting classification is employed to
characterise the complexity of a wide range of two-spin problems, fully
classifying the ferromagnetic case. In a further weakening of conservativity,
we also consider what happens if only the pinning functions are assumed to be
in $\mathcal{F}$ (instead of the two permissive unaries). We show that any set
of functions for which pinning is not sufficient to recover the two kinds of
permissive unaries must either have a very simple range, or must satisfy a
certain monotonicity condition. We exhibit a non-trivial example of a set of
functions satisfying the monotonicity condition.

**Authors: **Gramoz Goranci, Sebastian Krinninger **Download:** PDF**Abstract: **Spanning trees of low average stretch on the non-tree edges, as introduced by
Alon et al. [SICOMP 1995], are a natural graph-theoretic object. In recent
years, they have found significant applications in solvers for symmetric
diagonally dominant (SDD) linear systems. In this work, we provide the first
dynamic algorithm for maintaining such trees under edge insertions and
deletions to the input graph. Our algorithm has update time $ n^{1/2 + o(1)} $
and the average stretch of the maintained tree is $ n^{o(1)} $, which matches
the stretch in the seminal result of Alon et al.

Similar to Alon et al., our dynamic low-stretch tree algorithm employs a dynamic hierarchy of low-diameter decompositions (LDDs). As a major building block we use a dynamic LDD that we obtain by adapting the random-shift clustering of Miller et al. [SPAA 2013] to the dynamic setting. The major technical challenge in our approach is to control the propagation of updates within our hierarchy of LDDs. We believe that the dynamic random-shift clustering might be useful for independent applications. One of these potential applications follows from combining the dynamic clustering with the recent spanner construction of Elkin and Neiman [SODA 2017]. We obtain a fully dynamic algorithm for maintaining a spanner of stretch $ 2k - 1 $ and size $ O (n^{1 + 1/k} \log{n}) $ with amortized update time $ O (k \log^2 n) $ for any integer $ 2 \leq k \leq \log n $. Compared to the state-of-the art in this regime [Baswana et al. TALG '12], we improve upon the size of the spanner and the update time by a factor of $ k $.

**Authors: **Lailong Luo, Deke Guo, Richard T. B. Ma, Ori Rottenstreich, Xueshan Luo **Download:** PDF**Abstract: **Bloom filter (BF) has been widely used to support membership query, i.e., to
judge whether a given element x is a member of a given set S or not. Recent
years have seen a flourish design explosion of BF due to its characteristic of
space-efficiency and the functionality of constant-time membership query. The
existing reviews or surveys mainly focus on the applications of BF, but fall
short in covering the current trends, thereby lacking intrinsic understanding
of their design philosophy. To this end, this survey provides an overview of BF
and its variants, with an emphasis on the optimization techniques. Basically,
we survey the existing variants from two dimensions, i.e., performance and
generalization. To improve the performance, dozens of variants devote
themselves to reducing the false positives and implementation costs. Besides,
tens of variants generalize the BF framework in more scenarios by diversifying
the input sets and enriching the output functionalities. To summarize the
existing efforts, we conduct an in-depth study of the existing literature on BF
optimization, covering more than 60 variants. We unearth the design philosophy
of these variants and elaborate how the employed optimization techniques
improve BF. Furthermore, comprehensive analysis and qualitative comparison are
conducted from the perspectives of BF components. Lastly, we highlight the
future trends of designing BFs. This is, to the best of our knowledge, the
first survey that accomplishes such goals.

**Authors: **Warut Suksompong, Charles E. Leiserson, Tao B. Schardl **Download:** PDF**Abstract: **This paper investigates a variant of the work-stealing algorithm that we call
the localized work-stealing algorithm. The intuition behind this variant is
that because of locality, processors can benefit from working on their own
work. Consequently, when a processor is free, it makes a steal attempt to get
back its own work. We call this type of steal a steal-back. We show that the
expected running time of the algorithm is $T_1/P+O(T_\infty P)$, and that under
the "even distribution of free agents assumption", the expected running time of
the algorithm is $T_1/P+O(T_\infty\lg P)$. In addition, we obtain another
running-time bound based on ratios between the sizes of serial tasks in the
computation. If $M$ denotes the maximum ratio between the largest and the
smallest serial tasks of a processor after removing a total of $O(P)$ serial
tasks across all processors from consideration, then the expected running time
of the algorithm is $T_1/P+O(T_\infty M)$.

**Authors: **Peter Peter Bürgisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson **Download:** PDF**Abstract: **We present a polynomial time algorithm to approximately scale tensors of any
format to arbitrary prescribed marginals (whenever possible). This unifies and
generalizes a sequence of past works on matrix, operator and tensor scaling.
Our algorithm provides an efficient weak membership oracle for the associated
moment polytopes, an important family of implicitly-defined convex polytopes
with exponentially many facets and a wide range of applications. These include
the entanglement polytopes from quantum information theory (in particular, we
obtain an efficient solution to the notorious one-body quantum marginal
problem) and the Kronecker polytopes from representation theory (which capture
the asymptotic support of Kronecker coefficients). Our algorithm can be applied
to succinct descriptions of the input tensor whenever the marginals can be
efficiently computed, as in the important case of matrix product states or
tensor-train decompositions, widely used in computational physics and numerical
mathematics.

We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries.

**Authors: **Djamal Belazzougui, Paolo Boldi, Rasmus Pagh, Sebastiano Vigna **Download:** PDF**Abstract: **It has been shown in the indexing literature that there is an essential
difference between prefix/range searches on the one hand, and predecessor/rank
searches on the other hand, in that the former provably allows faster query
resolution. Traditionally, prefix search is solved by data structures that are
also dictionaries---they actually contain the strings in $S$. For very large
collections stored in slow-access memory, we propose much more compact data
structures that support \emph{weak} prefix searches---they return the ranks of
matching strings provided that \emph{some} string in $S$ starts with the given
prefix. In fact, we show that our most space-efficient data structure is
asymptotically space-optimal. Previously, data structures such as String
B-trees (and more complicated cache-oblivious string data structures) have
implicitly supported weak prefix queries, but they all have query time that
grows logarithmically with the size of the string collection. In contrast, our
data structures are simple, naturally cache-efficient, and have query time that
depends only on the length of the prefix, all the way down to constant query
time for strings that fit in one machine word. We give several applications of
weak prefix searches, including exact prefix counting and approximate counting
of tuples matching conjunctive prefix conditions.

Several years ago, I worked on a project where the goal was to try to come up with an "equitable" version of a measure of dependence; the idea was you could take a large multi-dimensional data set, score the dependence for each pair of variables, rank the pairs by their score, and then look at the top-scoring paris to try to determine the most interesting relationship to follow up on in further work. We were motivated by the need for data exploration tools for multi-dimensional data sets.

After a large number of years, we've updated the site http://www.exploredata.net/ , with some (finally) recently published papers, and new versions of the code that are faster, more accurate, and can do additional tasks (what we call TIC as well as MIC). Our technical information subpage has links to papers, including the relatively recent papers in JMLR and the Annals of Applied Statistics. Our MINE-Application page contains links to our new version of the code, as well as links to other versions (such as minepy, a library that has APIs in python and Matlab).

The incentive for all this was, in part, one of the co-authors, Yakir Reshef, finishing up his PhD thesis. Congratulations Yakir!

After a large number of years, we've updated the site http://www.exploredata.net/ , with some (finally) recently published papers, and new versions of the code that are faster, more accurate, and can do additional tasks (what we call TIC as well as MIC). Our technical information subpage has links to papers, including the relatively recent papers in JMLR and the Annals of Applied Statistics. Our MINE-Application page contains links to our new version of the code, as well as links to other versions (such as minepy, a library that has APIs in python and Matlab).

The incentive for all this was, in part, one of the co-authors, Yakir Reshef, finishing up his PhD thesis. Congratulations Yakir!

A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If can be partitioned into copies of we say that tiles . Here is a simpe example. Let consists of … Continue reading

A tile is a finite subset of . We can ask if can or cannot be partitioned into copies of . If can be partitioned into copies of we say that tiles .

Here is a simpe example. Let consists of 24 points of the 5 by 5 planar grid minus the center point. cannot tile .

**Test your intuition:** Does tiles for some ?

If you prefer you can think about the simpler case of consisting of eight points: the 3 by 3 grid minus the center.

I forgot to add polls…

Mitali Bafna, Chi-Ning Chou, and Zhao Song wrote scribe notes for my lectures on the Dinur et al proof of the 2 to 2 conjecture (see the DKKMS and KMS papers, though this presentation follows a different, and in my view simpler, approach.)

“Scribe notes” is really an understatement. In a heroic work, Mitali, Chi-Ning and Zhao supplied many more details and proofs (and much better exposition, including figures and comments) than I actually did in my talks. (One proof is still missing, but hopefully it will be updated in a few weeks or so.)

The notes assume no background in prior works on PCP and unique games, and can be very useful for anyone interested in these recent breakthroughs.