Related papers: Symmetric Exponential Time Requires Near-Maximum C…
We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset…
Reversible circuits have been studied extensively and intensively, and have plenty of applications in various areas, such as digital signal processing, cryptography, and especially quantum computing. In 2003, the lower bound $\Omega(2^n…
Given an array of distinct integers $A[1\ldots n]$, the Range Minimum Query (RMQ) problem requires us to construct a data structure from $A$, supporting the RMQ query: given an interval $[a,b]\subseteq[1,n]$, return the index of the minimum…
We prove conditional near-quadratic running time lower bounds for approximate Bichromatic Closest Pair with Euclidean, Manhattan, Hamming, or edit distance. Specifically, unless the Strong Exponential Time Hypothesis (SETH) is false, for…
We show that there is no $2^{o(k^2)} n^{O(1)}$ time algorithm for Independent Set on $n$-vertex graphs with rank-width $k$, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the $2^{O(k^2)} n^{O(1)}$ time algorithm…
We show that sharp thresholds for Boolean functions directly imply average-case circuit lower bounds. More formally we show that any Boolean function exhibiting a sharp enough threshold at \emph{arbitrary} critical density cannot be…
How hard is it to estimate a discrete-time signal $(x_{1}, ..., x_{n}) \in \mathbb{C}^n$ satisfying an unknown linear recurrence relation of order $s$ and observed in i.i.d. complex Gaussian noise? The class of all such signals is…
Policy evaluation in reinforcement learning is often conducted using two-timescale stochastic approximation, which results in various gradient temporal difference methods such as GTD(0), GTD2, and TDC. Here, we provide convergence rate…
In the setting of quasi-static multiple-input multiple-output (MIMO) channels, we consider the high signal-to-noise ratio (SNR) asymptotic complexity required by the sphere decoding (SD) algorithm for decoding a large class of full rate…
We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…
We give the first super-polynomial separation in the power of bounded-depth boolean formulas vs. circuits. Specifically, we consider the problem Distance $k(n)$ Connectivity, which asks whether two specified nodes in a graph of size $n$ are…
We consider the minimum makespan problem for $n$ tasks and two unrelated parallel selfish machines. Let $R_n$ be the best approximation ratio of randomized monotone scale-free algorithms. This class contains the most efficient algorithms…
We examine a parameterized complexity class for randomized computation where only the error bound and not the full runtime is allowed to depend more than polynomially on the parameter, based on a proposal by Kwisthout in [15,16]. We prove…
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
We develop a polynomial method on finite fields to amplify the hardness of spare sets in nondeterministic time complexity classes on a randomized streaming model. One of our results shows that if there exists a $2^{n^{o(1)}}$-sparse set in…
A fundamental question in the theory of reinforcement learning is: suppose the optimal $Q$-function lies in the linear span of a given $d$ dimensional feature mapping, is sample-efficient reinforcement learning (RL) possible? The recent and…
We introduce the polynomial coefficient matrix and identify maximum rank of this matrix under variable substitution as a complexity measure for multivariate polynomials. We use our techniques to prove super-polynomial lower bounds against…
The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called…
We reduce non-deterministic time $T \ge 2^n$ to a 3SAT instance $\phi$ of quasilinear size $|\phi| = T \cdot \log^{O(1)} T$ such that there is an explicit circuit $C$ that on input an index $i$ of $\log |\phi|$ bits outputs the $i$th…