Yuval Filmus

• PhD
• Professor (Assistant) at Technion – Israel Institute of Technology

A generalized polymorphism of a predicate $P \subseteq \{0,1\}^m$ is a tuple of functions $f_1,\dots,f_m\colon \{0,1\}^n \to \{0,1\}$ satisfying the following property: If $x^{(1)},\dots,x^{(m)} \in \{0,1\}^n$ are such that $(x^{(1)}_i,\dots,x^{(m)}_i) \in P$ for all $i$, then also $(f_1(x^{(1)}),\dots,f_m(x^{(m)})) \in P$. We show that if $f_1,\do...

In a seminal work, Buhrman et al. (STOC 2014) defined the class $CSPACE(s,c)$ of problems solvable in space $s$ with an additional catalytic tape of size $c$, which is a tape whose initial content must be restored at the end of the computation. They showed that uniform $TC^1$ circuits are computable in catalytic logspace, i.e., $CL=CSPACE(O(\log{n}...

Dokow and Holzman determined which predicates over $\{0, 1\}$ satisfy an analog of Arrow's theorem: all unanimous aggregators are dictatorial. Szegedy and Xu, extending earlier work of Dokow and Holzman, extended this to predicates over arbitrary finite alphabets. Mossel extended Arrow's theorem in an orthogonal direction, determining all aggregato...

We consider two classic problems: maximum coverage and monotone submodular maximization subject to a cardinality constraint. [Nemhauser--Wolsey--Fisher '78] proved that the greedy algorithm provides an approximation of $1-1/e$ for both problems, and it is known that this guarantee is tight ([Nemhauser--Wolsey '78; Feige '98]). Thus, one would natur...

We give a structure theorem for Boolean functions on the $p$-biased hypercube which are $\epsilon$-close to degree $d$ in $L_2$, showing that they are close to sparse juntas. Our structure theorem implies that such functions are $O(\epsilon^{C_d} + p)$-close to constant functions. We pinpoint the exact value of the constant $C_d$. We also give an a...

It is a classical result that the inner product function cannot be computed by an AC0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm AC}^0$$\end{document} circuit....

Let Dn,k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{n,k}$$\end{document} be the set of all permutations of the symmetric group Sn\documentclass[12pt]{minimal} \u...

The hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more. So far, variants of this inequality have been proved mainly for product spaces, which raises the question of whether analogous results hold over non-product domains. We co...

A subcube partition is a partition of the Boolean cube $\{0,1\}^n$ into subcubes. A subcube partition is irreducible if the only sub-partitions whose union is a subcube are singletons and the entire partition. A subcube partition is tight if it “mentions” all coordinates. We study extremal properties of tight irreducible subcube partitions: minimal...

An affine vector space partition of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\textrm{AG}\,}}(n,q)$$\end{document} is a set of proper affine subspaces that pa...

We determine all $m$-ary Boolean functions $f_0,\ldots,f_m$ and $n$-ary Boolean functions $g_0,\ldots,g_n$ satisfying the equation \[ f_0(g_1(z_{11},\ldots,z_{1m}),\ldots,g_n(z_{n1},\ldots,z_{nm})) = g_0(f_1(z_{11},\ldots,z_{n1}),\ldots,f_m(z_{1m},\ldots,z_{nm})), \] for all Boolean inputs $\{ z_{ij} : i \in [n], j \in [m] \}$. This extends charact...

A circuit $\mathcal{C}$ samples a distribution $\mathbf{X}$ with an error $\epsilon$ if the statistical distance between the output of $\mathcal{C}$ on the uniform input and $\mathbf{X}$ is $\epsilon$. We study the hardness of sampling a uniform distribution over the set of $n$-bit strings of Hamming weight $k$ denoted by $\mathbf{U}^n_k$ for _deci...

We show that a Boolean degree~$d$ function on the slice $\binom{[n]}{k}$ is a junta if $k \geq 2d$, and that this bound is sharp. We prove a similar result for $A$-valued degree~$d$ functions for arbitrary finite $A$, and for functions on an infinite analog of the slice.

A classical result in online learning characterizes the optimal mistake bound achievable by deterministic learners using the Littlestone dimension (Littlestone '88). We prove an analogous result for randomized learners: we show that the optimal expected mistake bound in learning a class $\mathcal{H}$ equals its randomized Littlestone dimension, whi...

Hitting formulas have been studied in many different contexts at least since [Iwama,89]. A hitting formula is a set of Boolean clauses such that any two of them cannot be simultaneously falsified. [Peitl,Szeider,05] conjectured that hitting formulas should contain the hardest formulas for resolution. They supported their conjecture with experimenta...

A \emph{subcube partition} is a partition of the Boolean cube $\{0,1\}^n$ into subcubes. A subcube partition is irreducible if the only sub-partitions whose union is a subcube are singletons and the entire partition. A subcube partition is tight if it "mentions" all coordinates. We study extremal properties of tight irreducible subcube partitions:...

We give a characterization of the largest $2$-intersecting families of permutations of $\{1,2,\ldots,n\}$ and of perfect matchings of the complete graph $K_{2n}$ for all $n \geq 2$.

Given a learning task where the data is distributed among several parties, communication is one of the fundamental resources which the parties would like to minimize. We present a distributed boosting algorithm which is resilient to a limited amount of noise. Our algorithm is similar to classical boosting algorithms, although it is equipped with a...

We show that a Boolean degree $d$ function on the slice $\binom{[n]}{k}$ is a junta if $k \geq 2d$, and that this bound is sharp. We prove a similar result for $A$-valued degree $d$ functions for arbitrary finite $A$, and for functions on an infinite analog of the slice.

We give simpler algebraic proofs of uniqueness for several Erd\H{o}s-Ko-Rado results, i.e., that the canonically intersecting families are the only largest intersecting families. Using these techniques, we characterize the largest partially 2-intersecting families of perfect hypermatchings, resolving a recent conjecture of Meagher, Shirazi, and Ste...

We show that if $f\colon S_n \to \{0,1\}$ is $\epsilon$-close to linear in $L_2$ and $\mathbb{E}[f] \leq 1/2$ then $f$ is $O(\epsilon)$-close to a union of "mostly disjoint" cosets, and moreover this is sharp: any such union is close to linear. This constitutes a sharp Friedgut-Kalai-Naor theorem for the symmetric group. Using similar techniques, w...

In the distributional Twenty Questions game, Bob chooses a number $x$ from $1$ to $n$ according to a distribution $\mu$, and Alice (who knows $\mu$) attempts to identify $x$ using Yes/No questions, which Bob answers truthfully. Her goal is to minimize the expected number of questions. The optimal strategy for the Twenty Questions game corresponds t...

For a function $g\colon\{0,1\}^m\to\{0,1\}$, a function $f\colon \{0,1\}^n\to\{0,1\}$ is called a $g$-polymorphism if their actions commute: $f(g(\mathsf{row}_1(Z)),\ldots,g(\mathsf{row}_n(Z))) = g(f(\mathsf{col}_1(Z)),\ldots,f(\mathsf{col}_m(Z)))$ for all $Z\in\{0,1\}^{n\times m}$. The function $f$ is called an approximate polymorphism if this equ...

H\r{a}stad showed that any De Morgan formula (composed of AND, OR and NOT gates) shrinks by a factor of $O(p^{2})$ under a random restriction that leaves each variable alive independently with probability $p$ [SICOMP, 1998]. Using this result, he gave an $\widetilde{\Omega}(n^{3})$ formula size lower bound for the Andreev function, which, up to low...

We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.

We extend the definitions of complexity measures of functions to domains such as the symmetric group. The complexity measures we consider include degree, approximate degree, decision tree complexity, sensitivity, block sensitivity, and a few others. We show that these complexity measures are polynomially related for the symmetric group and for many...

The hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more. So far, variants of this inequality have been proved mainly for product spaces, which raises the question of whether analogous results hold over non-product domains. We co...

We construct an explicit family of 3XOR instances which is hard for $O(\sqrt{\log n})$ levels of the Sum-of-Squares hierarchy. In contrast to earlier constructions, which involve a random component, our systems can be constructed explicitly in deterministic polynomial time. Our construction is based on the high-dimensional expanders devised by Lubo...

We study the MaxRes rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p-simulates tree-like resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we d...

We study the MaxRes rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p-simulates tree-like resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting lower bounds from Res), we d...

2020 ACM. A function fg¶{0,1}n→ {0,1} is called an approximate AND-homomorphism if choosing x,ygn uniformly at random, we have that f(xg§ y) = f(x)g§ f(y) with probability at least 1-ϵ, where xg§ y = (x1g§ y1,...,xng§ yn). We prove that if fg¶ {0,1}n → {0,1} is an approximate AND-homomorphism, then f is -close to either a constant function or an AN...

In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for \emph{general} low-degree functions, with no constraints on the influences. We show that any real-valued function on the slice, whose degree when written as a harmonic multi-linea...

One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of its eigenvalues. It is easily seen that the Hoffman bound is sharp on the tensor power of a graph whenever it is sharp for the original graph. In this paper, we introduc...

In a recent breakthrough paper Braverman et al. (in: STOC’13, pp 151–160, 2013) developed a local characterization for the zero-error information complexity in the two-party model, and used it to compute the exact internal and external information complexity of the 2-bit AND function. In this article, we extend their results on AND function to the...

A function $f\colon\{0,1\}^n\to \{0,1\}$ is called an approximate AND-homomorphism if choosing ${\bf x},{\bf y}\in\{0,1\}^n$ randomly, we have that $f({\bf x}\land {\bf y}) = f({\bf x})\land f({\bf y})$ with probability at least $1-\epsilon$, where $x\land y = (x_1\land y_1,\ldots,x_n\land y_n)$. We prove that if $f\colon \{0,1\}^n \to \{0,1\}$ is...

The Friedgut–Kalai–Naor (FKN) theorem states that if ƒ is a Boolean function on the Boolean cube which is close to degree one, then ƒ is close to a dictator , a function depending on a single coordinate. The author has extended the theorem to the slice , the subset of the Boolean cube consisting of all vectors with fixed Hamming weight. We extend t...

We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. and Wu et al. The only query-to-communication lifting resul...

The seminal result of Kahn, Kalai and Linial shows that a coalition of $O(\frac{n}{\log n})$ players can bias the outcome of any Boolean function $\{0,1\}^n \to \{0,1\}$ with respect to the uniform measure. We extend their result to arbitrary product measures on $\{0,1\}^n$, by combining their argument with a completely different argument that hand...

A basic combinatorial interpretation of Shannon’s entropy function is via the “20 questions” game. This cooperative game is played by two players, Alice and Bob: Alice picks a distribution π over the numbers {1, …, n}, and announces it to Bob. She then chooses a number x according to π, and Bob attempts to identify x using as few Yes/No queries as...

Weighted voting games (WVGs) are a class of cooperative games that capture settings of group decision making in various domains, such as parliaments or committees. Earlier work has revealed that the effective decision making power, or influence of agents in WVGs is not necessarily proportional to their weight. This gave rise to measures of influenc...

Twenty questions' is a guessing game played by two players: Bob thinks of an integer between $1$ and $n$, and Alice's goal is to recover it using a minimal number of Yes/No questions. Shannon's entropy has a natural interpretation in this context. It characterizes the average number of questions used by an optimal strategy in the distributional var...

Let $\kappa \in \mathbb{N}_+^\ell$ satisfy $\kappa_1 + \dots + \kappa_\ell = n$ and let $\mathcal{U}_\kappa$ denote the "multislice" of all strings $u$ in $[\ell]^n$ having exactly $\kappa_i$ coordinates equal to $i$, for all $i \in [\ell]$. Consider the Markov chain on $\mathcal{U}_\kappa$, where a step is a random transposition of two coordinates...

The Friedgut-Kalai-Naor (FKN) theorem states that if $f$ is a Boolean function on the Boolean cube which is close to degree 1, then $f$ is close to a dictator, a function depending on a single coordinate. The author has extended the theorem to the slice, the subset of the Boolean cube consisting of all vectors with fixed Hamming weight. We extend t...

We extend the Sauer-Shelah-Perles lemma to an abstract setting that is formalized using the language of lattices. Our extension applies to all finite lattices with nonvanishing M\"obius function, a rich class of lattices which includes all geometric lattices (or matroids) as a special case. For example, our extension implies the following result in...

We initiate the study of Boolean function analysis on high-dimensional expanders. We describe an analog of the Fourier expansion and of the Fourier levels on simplicial complexes, and generalize the FKN theorem to high-dimensional expanders. Our results demonstrate that a high-dimensional expanding complex $X$ can sometimes serve as a sparse model...

We initiate the study of Boolean function analysis on high-dimensional expanders. We give a random-walk based definition of high-dimensional expansion, which coincides with the earlier definition in terms of two-sided link expanders. Using this definition, we describe an analog of the Fourier expansion and the Fourier levels of the Boolean hypercub...

We show that a Boolean degree $d$ function on the slice $\binom{[n]}{k} = \{ (x_1,\ldots,x_n) \in \{0,1\} : \sum_{i=1}^n x_i = k \}$ is a junta, assuming that $k,n-k$ are large enough. This generalizes a classical result of Nisan and Szegedy on the hypercube. Moreover, we show that the maximum number of coordinates that a Boolean degree $d$ functio...

We show that a Boolean degree $d$ function on the slice $\binom{[n]}{k} = \{ (x_1,\ldots,x_n) \in \{0,1\} : \sum_{i=1}^n x_i = k \}$ is a junta, assuming that $k,n-k$ are large enough. This generalizes a classical result of Nisan and Szegedy on the hypercube. Moreover, we show that the maximum number of coordinates that a Boolean degree $d$ functio...

We investigate Boolean degree 1 functions for several classical association schemes, including Johnson graphs, Grassmann graphs, graphs from polar spaces, and bilinear forms graphs, as well as some other domains such as multislices (Young subgroups of the symmetric group). In some settings, Boolean degree 1 functions are also known as \textit{compl...

We investigate Boolean degree 1 functions for several classical association schemes, including Johnson graphs, Grassmann graphs, graphs from polar spaces, and bilinear forms graphs, as well as some other domains such as multislices (Young subgroups of the symmetric group). In some settings, Boolean degree 1 functions are also known as \textit{compl...

Agreement tests are a generalization of low degree tests that capture a local-to-global phenomenon, which forms the combinatorial backbone of most PCP constructions. In an agreement test, a function is given by an ensemble of local restrictions. The agreement test checks that the restrictions agree when they overlap, and the main question is whethe...

Nisan and Szegedy showed that low degree Boolean functions are juntas. Kindler and Safra showed that low degree functions which are almost Boolean are close to juntas. Their result holds with respect to $\mu_p$ for every constant $p$. When $p$ is allowed to be very small, new phenomena emerge. For example, the function $y_1 + \cdots + y_{\epsilon/p...

The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families for . We extend this theorem to the weighted setting, in which we consider unconstrained families on n points with respect to the measure given by . Our theorem give...

Ellis, Friedgut and Pilpel proved that for large enough $n$, a $t$-intersecting family of permutations contains at most $(n-t)!$ permutations. Their main theorem also states that equality holds only for $t$-cosets. We show that their proof of the characterization of extremal families is wrong. However, the characterization follows from a paper of E...

A basic combinatorial interpretation of Shannon's entropy function is via the "20 questions" game. This cooperative game is played by two players, Alice and Bob: Alice picks a distribution Π over the numbers {1,…,n}, and announces it to Bob. She then chooses a number x according to Π, and Bob attempts to identify x using as few Yes/No queries as po...

We introduce the Bhattacharya-Mesner rank of third order hypermatrices as a relaxation to the tensor rank and devise some upper bounds for the rank. We extend to third order hypermatrices the relation between linear dependence and their rank. We also derive necessary and sufficient conditions for the existence of third order hypermatrix inverse pai...

We introduce the Bhattacharya-Mesner rank of third order hypermatrices as a relaxation to the tensor rank and devise from it some bounds for the tensor rank. We use the Bhattacharya-Mesner rank to extend to third order hypermatrices the connection relating the rank to a notion of linear dependence. We also derive explicit necessary and sufficient c...

In a recent breakthrough paper [M. Braverman, A. Garg, D. Pankratov, and O. Weinstein, From information to exact communication, STOC'13] Braverman et al. developed a local characterization for the zero-error information complexity in the two party model, and used it to compute the exact internal and external information complexity of the 2-bit AND...

In a recent breakthrough paper [M. Braverman, A. Garg, D. Pankratov, and O. Weinstein, From information to exact communication, STOC'13] Braverman et al. developed a local characterization for the zero-error information complexity in the two party model, and used it to compute the exact internal and external information complexity of the 2-bit AND...

We extend to hypermatrices definitions and theorem from matrix theory. Our main result is an elementary derivation of the spectral decomposition of hypermatrices generated by arbitrary combinations of Kronecker products and direct sums of cubic side length 2 hypermatrices. The method is based on a generalization of Parseval's identity. We use this...

We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$. For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order $\Omega(h(\epsilon))$ and $O(h(\sqrt{\epsilon}))$. Here $h$ den...

We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$. For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order $\Omega(h(\epsilon))$ and $O(h(\sqrt{\epsilon}))$. Here $h$ den...

A basic combinatorial interpretation of Shannon's entropy function is via the "20 questions" game. This cooperative game is played by two players, Alice and Bob: Alice picks a distribution $\pi$ over the numbers $\{1,\ldots,n\}$, and announces it to Bob. She then chooses a number $x$ according to $\pi$, and Bob attempts to identify $x$ using as few...

The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a $k$-uniform $t$-intersecting family on $n$ points, and describes all optimal families. We extend this theorem to several other settings: the weighted case, the case of infinitely many points, and the Hamming scheme. The weighted Ahlswede-Khachat...

Weighted voting games (WVGs) are a class of cooperative games that capture settings of group decision making in various domains, such as parliaments or committees. Earlier work has revealed that the effective decision making power, or influence of agents in WVGs is not necessarily proportional to their weight. This gave rise to measures of influenc...

Let f: {-1, 1}ⁿ → [-1, 1] have degree d as a multilinear polynomial. It is well-known that the total influence of f is at most d. Aaronson and Ambainis asked whether the total L1 influence of f can also be bounded as a function of d. Bačkurs and Bavarian answered this question in the affirmative, providing a bound of O(d³) for general functions and...

We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective decision making systems. While easy to estimate empirically given the parameters of a weighted voting game, the Sha...

Our main result is an elementary derivation of the spectral decomposition of hypermatrices generated by arbitrary combinations of Kronecker products and direct sums of cubic hypermatrices of side length 2.

We prove that Boolean functions on $S_n$, whose Fourier transform is highly concentrated on irreducible representations indexed by partitions of $n$ whose largest part has size at least $n-t$, are close to being unions of cosets of stabilizers of $t$-tuples. We also obtain an edge-isoperimetric inequality for the transposition graph on $S_n$ which...

Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time O(n2.3755). Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le~Gall has led to an improved algorithm running in time O(n2.3729). These algorithms are obtained by analyzing higher and higher tensor powers...

We prove that a balanced Boolean function on S_n whose Fourier transform is highly concentrated on the first two irreducible representations of S_n, is close in structure to a dictatorship, a function which is determined by the image or pre-image of a single element. As a corollary, we obtain a stability result concerning extremal isoperimetric set...

We prove an invariance principle for functions on a slice of the Boolean cube, which is the set of all vectors {0,1}^n with Hamming weight k. Our invariance principle shows that a low-degree, low-influence function has similar distributions on the slice, on the entire Boolean cube, and on Gaussian space. Our proof relies on a combination of ideas f...

Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time $O(n^{2.3755})$. Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le Gall has led to an improved algorithm running in time $O(n^{2.3729})$. These algorithms are obtained by analyzing higher and higher ten...

The Friedgut--Kalai--Naor theorem states that if a Boolean function $f\colon \{0,1\}^n \to \{0,1\}$ is close (in $L^2$-distance) to an affine function $\ell(x_1,...,x_n) = c_0 + \sum_i c_i x_i$, then $f$ is close to a Boolean affine function (which necessarily depends on at most one coordinate). We prove a similar theorem for functions defined over...

In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of CNF formulas is always an upper bound on the width needed to refute them. Their proof is beautiful but somewhat mysterious in that it relies heavily on tools from finite model theory. We give an alternative, com...

We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote process. We characterize the impact of changing the quota (i.e., the minimum number of seats in the parliamen...

We present a simple, explicit orthogonal basis of eigenvectors for the Johnson and Kneser graphs, based on Young’s orthogonal representation of the symmetric group. Our basis can also be viewed as an orthogonal basis for the vector space of all functions over a slice of the Boolean hypercube (a set of the form f(x1...,xn) ɛ {0, 1}n : ∑i xi= k}), wh...

Top-i voting is a common form of preference elicitation due to its conceptual simplicity both on the voters' side and on the decision maker's side. In a typical setting, given a set of candidates, the voters are required to submit only the k-length prefixes of their intrinsic rankings of the candidates. The decision maker then tries to correctly pr...

We describe here a rudimentary sage implementation of the Bhattacharya-Mesner hypermatrix algebra package.

We present an optimal, combinatorial 1 − 1/e approximation algorithm for monotone submodular op-timization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pál and Vondrák, 2008), our algorithm is extremely simple and requires no rounding. It consists of the greedy algorithm followed by local search. Both...

An approximate computation of a Boolean function by a circuit or switching network is a computation in which the function is computed correctly on the majority of the inputs (rather than on all inputs). Besides being interesting in their own right, lower bounds for approximate computation have proved useful in many sub areas of complexity theory, s...

A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how to construct effectively a code better than a given sequence of codes, in a certain precise sense. As an applic...

Top-k voting is an especially natural form of partial vote elicitation in which only length k prefixes of rankings are elicited. We analyze the ability of top-k vote elicitation to correctly determine true winners, with high probability, given probabilistic models of voter preferences and candidate availability. We provide bounds on the minimal val...

We devise a method for proving inequalities on submodular functions, with a term rewriting flavor. Our method comprises of the following steps: (1) start with a linear combination X of the values of the function; (2) define a set of simplification rules; (3) conclude that X⩾YX⩾Y, where Y is a linear combination of a small number of terms which cann...

During the last decade, an active line of research in proof complexity has been into the space complexity of proofs and how space is related to other measures. By now these aspects of resolution are fairly well understood, but many open problems remain for the related but stronger polynomial calculus (PC/PCR) proof system. For instance, the space c...

We prove that Boolean functions on $S_{n}$ whose Fourier transform is highly concentrated on the first two irreducible representations of $S_n$, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku, and f...

We prove that Boolean functions on S_n whose Fourier transform is highly concentrated on the first two irreducible representations of S_n, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku, and first p...

In 1990, Subramanian [1990] defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem (CCV). He and Mayr showed that NL ⊆ CC ⊆ P, and proved that in addition to CCV several other problems are complete for CC, including the stable marriage problem, and finding the lexicographically first maxim...

During the last decade, an active line of research in proof complexity has been to study space complexity and time space trade-offs for proofs. Besides being a natural complexity measure of intrinsic interest, space is also an important issue in SAT solving. For the polynomial calculus proof system, the only previously known space lower bound is fo...

In this demonstration, we showcase the technologies that we are building at Yahoo! for Web-scale Information Extraction. Given any new Website, containing semi-structured information about a pre-specified set of schemas, we show how to populate objects in the corresponding schema by automatically extracting information from the Website.

We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is extremely simple and requires no rounding. It consists of the greedy algorithm followed by local search. Both pha...

We present an optimal, combinatorial 1-1/e approximation algorithm for maximum coverage over a matroid constraint, using non-oblivious local search. G. Calinescu et al. [“Maximizing a monotone submodular function subject to a matroid constraint”, in: STOC’08. Proceedings of the 40th annual ACM symposium on theory of computing. New York, NY: Associa...