相关论文: A Lower Bound for Estimating High Moments of a Dat…
We present a new approach for finding matchings in dense graphs by building on Szemer\'edi's celebrated Regularity Lemma. This allows us to obtain non-trivial albeit slight improvements over longstanding bounds for matchings in streaming…
We fully determine the communication complexity of approximating matrix rank, over any finite field $\mathbb{F}$. We study the most general version of this problem, where $0\leq r<R\leq n$ are given integers, Alice and Bob's inputs are…
We investigate the limits of one of the fundamental ideas in data structures: fractional cascading. This is an important data structure technique to speed up repeated searches for the same key in multiple lists and it has numerous…
This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order…
Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…
We investigate one of the most basic problems in streaming algorithms: approximating the number of elements in the stream. In 1978, Morris famously gave a randomized algorithm achieving a constant-factor approximation error for streams of…
To get estimators that work within a certain error bound with high probability, a common strategy is to design one that works with constant probability, and then boost the probability using independent repetitions. Important examples of…
Least box number coverage problem for calculating dimension of fractal networks is a NP-hard problem. Meanwhile, the time complexity of random ball coverage for calculating dimension is very low. In this paper we strictly present the upper…
It is shown that solutions to the anisotropic least gradient problem for boundary data $f \in L^p(\partial\Omega)$ lie in $L^{\frac{Np}{N-1}}(\Omega)$; the exponent is shown to be optimal. Moreover, the solutions are shown to be locally…
The threshold degree of a function f:{0,1}^n->{-1,+1} is the least degree of a real polynomial p with f(x)=sgn p(x). We prove that the intersection of two halfspaces on {0,1}^n has threshold degree Omega(n), which matches the trivial upper…
It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the…
We present improved upper bounds for the size of relative (p,Epsilon)-approximation for range spaces with the following property: For any (finite) range space projected onto (that is, restricted to) a ground set of size n and for any…
A range counting problem is specified by a set $P$ of size $|P| = n$ of points in $\mathbb{R}^d$, an integer weight $x_p$ associated to each point $p \in P$, and a range space ${\cal R} \subseteq 2^{P}$. Given a query range $R \in {\cal…
Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of $n$ items from a data universe equipped with a total order, the task is to compute a sketch (data…
This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with…
For an arbitrary family of predicates $\mathcal{F} \subseteq \{0,1\}^{[q]^k}$ and any $\epsilon > 0$, we prove a single-pass, linear-space streaming lower bound against the gap promise problem of distinguishing instances of…
An ordering constraint satisfaction problem (OCSP) is defined by a family $\mathcal{F}$ of predicates mapping permutations on $\{1,\ldots,k\}$ to $\{0,1\}$. An instance of Max-OCSP($\mathcal{F}$) on $n$ variables consists of a list of…
In this work, we use the matrix formulation of the Permutation Flowshop Scheduling Problem with makespan minimization to derive an upper bound and a general framework for obtaining lower bounds. The proposed framework involves solving a…