Binary logarithm ≈ Binary logarithm
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On the Convergence of FedAvg on Non-IID Data Open
Federated learning enables a large amount of edge computing devices to jointly learn a model without data sharing. As a leading algorithm in this setting, Federated Averaging (\texttt{FedAvg}) runs Stochastic Gradient Descent (SGD) in para…
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Distributed Statistical Machine Learning in Adversarial Settings: Byzantine Gradient Descent Open
We consider the problem of distributed statistical machine learning in adversarial settings, where some unknown and time-varying subset of working machines may be compromised and behave arbitrarily to prevent an accurate model from being l…
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Solving Linear Programs in the Current Matrix Multiplication Time Open
This article shows how to solve linear programs of the form min Ax = b , x ≥ 0 c ⊤ x with n variables in time O * (( n ω + n 2.5−α/2 + n 2+1/6 ) log ( n /δ)), where ω is the exponent of matrix multiplication, α is the dual exponent of matr…
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Communication Steps for Parallel Query Processing Open
We study the problem of computing conjunctive queries over large databases on parallel architectures without shared storage. Using the structure of such a query q and the skew in the data, we study tradeoffs between the number of processor…
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Log-concave sampling: Metropolis-Hastings algorithms are fast Open
We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by simulati…
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Scalability of Continuous Active Learning for Reliable High-Recall Text Classification Open
For finite document collections, continuous active learning ('CAL') has been observed to achieve high recall with high probability, at a labeling cost asymptotically proportional to the number of relevant documents. As the size of the coll…
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Space-Optimal Majority in Population Protocols Open
Population protocols are a popular model of distributed computing, in which n agents with limited local state interact randomly, and cooperate to collectively compute global predicates. Inspired by recent developments in DNA programming, a…
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Designing FPT Algorithms for Cut Problems Using Randomized Contractions Open
We introduce a new technique for designing xed-parameter algorithms for cut problems, called randomized contractions. We apply our framework to obtain the rst xed-parameter algorithms (FPT algorithms) with exponential speed up for the Stei…
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Dynamic Approximate All-Pairs Shortest Paths: Breaking the $O(mn)$ Barrier and Derandomization Open
We study dynamic $(1+\\epsilon)$-approximation algorithms for the all-pairs\nshortest paths problem in unweighted undirected $n$-node $m$-edge graphs under\nedge deletions. The fastest algorithm for this problem is a randomized\nalgorithm …
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MST in Log-Star Rounds of Congested Clique Open
We present a randomized algorithm that computes a Minimum Spanning Tree (MST) in O(log* n) rounds, with high probability, in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially eac…
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Beyond matroids: secretary problem and prophet inequality with general constraints Open
We study generalizations of the ``Prophet Inequality'' and ``Secretary Problem'', where the algorithm is restricted to an arbitrary downward-closed set system. For 0,1 values, we give O(n)-competitive algorithms for both problems. This is …
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On Estimating Maximum Matching Size in Graph Streams Open
We study the problem of estimating the maximum matching size in graphs whose edges are revealed in a streaming manner. We consider both insertion-only streams and dynamic streams and present new upper and lower bound results for both model…
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On the Choice of the Update Strength in Estimation-of-Distribution Algorithms and Ant Colony Optimization Open
Probabilistic model-building Genetic Algorithms (PMBGAs) are a class of metaheuristics that evolve probability distributions favoring optimal solutions in the underlying search space by repeatedly sampling from the distribution and updatin…
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Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data Open
In this paper, we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions. Such a network rep…
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Faster Polynomial Multiplication over Finite Fields Open
Polynomials over finite fields play a central role in algorithms for cryptography, error correcting codes, and computer algebra. The complexity of multiplying such polynomials is still a major open problem. Let p be a prime, and let M p ( …
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Chebyshev polynomials, moment matching, and optimal estimation of the unseen Open
We consider the problem of estimating the support size of a discrete distribution whose minimum nonzero mass is at least $\\frac{1}{k}$. Under the independent sampling model, we show that the sample complexity, that is, the minimal sample …
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Slightly Superexponential Parameterized Problems Open
A central problem in parameterized algorithms is to obtain algorithms\n with running time $f(k)\\cdot n^{O(1)}$ such that $f$ is as slow growing\nfunction of the parameter $k$ as possible. In particular, a large number of\nbasic parameteri…
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Sparsifying Distributed Algorithms with Ramifications in Massively Parallel Computation and Centralized Local Computation Open
We introduce a method for “sparsifying” distributed algorithms and exhibit how it leads to improvements that go past known barriers in two algorithmic settings of large-scale graph processing: Massively Parallel Computation (MPC), and Loca…
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Time-Space Trade-offs in Population Protocols Open
Population protocols are a popular model of distributed computing, in which randomly-interacting agents with little computational power cooperate to jointly perform computational tasks. Inspired by developments in molecular computation, an…
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The Complexity of (Δ+1) Coloring in Congested Clique, Massively Parallel Computation, and Centralized Local Computation Open
In this paper, we present new randomized algorithms that improve the complexity of the classic (Δ+1)-coloring problem, and its generalization (Δ+1)-list-coloring, in three well-studied models of distributed, parallel, and centralized compu…
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Coresets Meet EDCS: Algorithms for Matching and Vertex Cover on Massive Graphs Open
There is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on massive graphs. For massive inputs, several different computational models have been introdu…
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Distributed Degree Splitting, Edge Coloring, and Orientations Open
We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly. Our finding…
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Optimal time and space leader election in population protocols Open
Full verions, including all proofs
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Sublogarithmic Distributed Algorithms for Lov\\'asz Local lemma, and the\n Complexity Hierarchy Open
Locally Checkable Labeling (LCL) problems include essentially all the classic\nproblems of $\\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening\nrevelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded\…
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Towards a Definitive Measure of Repetitiveness Open
Unlike in statistical compression, where Shannon's entropy is a definitive lower bound, no such clear measure exists for the compressibility of repetitive sequences. Since statistical entropy does not capture repetitiveness, ad-hoc measure…
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Parallel Batch-Dynamic Graph Connectivity Open
In this paper, we study batch parallel algorithms for the dynamic\nconnectivity problem, a fundamental problem that has received considerable\nattention in the sequential setting. The most well known sequential algorithm\nfor dynamic conne…
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Threesomes, Degenerates, and Love Triangles Open
The 3SUM problem is to decide, given a set of n real numbers, whether any three sum to zero. It is widely conjectured that a trivial O ( n 2 )-time algorithm is optimal on the Real RAM, and optimal even in the nonuniform linear decision tr…
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An <i>O</i> ( <i>m</i> log <i>n</i> ) Algorithm for Computing Stuttering Equivalence and Branching Bisimulation Open
We provide a new algorithm to determine stuttering equivalence with time complexity O ( m log n ), where n is the number of states and m is the number of transitions of a Kripke structure. This algorithm can also be used to determine branc…
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Polynomial Multiplication over Finite Fields in Time \( O(n \log n \) Open
Assuming a widely believed hypothesis concerning the least prime in an arithmetic progression, we show that polynomials of degree less than \( n \) over a finite field \( \mathbb {F}_q \) with \( q \) elements can be multiplied in time \( …
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A Logarithmic Additive Integrality Gap for Bin Packing Open
For bin packing, the input consists of n items with sizes s1,…, sn ∊ [0,1] which have to be assigned to a minimum number of bins of size 1. Recently, the second author gave an LP-based polynomial time algorithm that employed techniques fro…