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In large-scale classification problems, the data set always be faced with frequent updates when a part of the data is added to or removed from the original data set. In this case, conventional incremental learning, which updates an existing…

Machine Learning · Computer Science 2021-01-15 Kaichen Zhou , Shiji Song , Gao Huang , Wu Cheng , Quan Zhou

The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus…

Logic in Computer Science · Computer Science 2019-01-16 Daniel Hausmann , Lutz Schröder

A \emph{covering array} is an $N \times k$ array of elements from a $v$-ary alphabet such that every $N \times t$ subarray contains all $v^t$ tuples from the alphabet of size $t$ at least $\lambda$ times; this is denoted as $\CA_\lambda(N;…

Combinatorics · Mathematics 2023-06-06 Mason R. Calbert , Ryan E. Dougherty

The dynamic optimality conjecture, postulating the existence of an $O(1)$-competitive online algorithm for binary search trees (BSTs), is among the most fundamental open problems in dynamic data structures. Despite extensive work and some…

Data Structures and Algorithms · Computer Science 2019-12-24 Parinya Chalermsook , Julia Chuzhoy , Thatchaphol Saranurak

Radio network deployment and coverage optimization are critical to next-generation wireless networks. In this paper, the problem of optimally deciding on whether to install additional small cells or to upgrade current macrocell base…

Information Theory · Computer Science 2014-06-24 Xiangxiang Xu , Xiujun Zhang , Walid Saad , Yifei Zhao , Shidong Zhou

We construct $n$-node graphs on which any $O(n)$-size spanner has additive error at least $+\Omega(n^{3/17})$, improving on the previous best lower bound of $\Omega(n^{1/7})$ [Bodwin-Hoppenworth FOCS '22]. Our construction completes the…

Data Structures and Algorithms · Computer Science 2024-04-30 Greg Bodwin , Gary Hoppenworth , Virginia Vassilevska Williams , Nicole Wein , Zixuan Xu

In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…

Data Structures and Algorithms · Computer Science 2016-04-11 Paweł Gawrychowski , Adam Karczmarz , Tomasz Kociumaka , Jakub Łącki , Piotr Sankowski

We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…

Computational Complexity · Computer Science 2016-07-05 Tonnian Pitassi , Iddo Tzameret

We briefly review known results on upper bounds for the minimal domination number $\gamma_n$ of a hypercube of dimension $n$, then present a new method for constructing dominating sets. Write $n =2^{\hat{n}}-1 +{\check{n}}$ with $0\leq…

Combinatorics · Mathematics 2024-09-24 Zachary DeVivo , Robert K. Hladky

Data mixing--the strategic reweighting of training domains--is a critical component in training robust machine learning models. This problem is naturally formulated as a bilevel optimization task, where the outer loop optimizes domain…

Machine Learning · Computer Science 2026-02-24 Rudrajit Das , Neel Patel , Meisam Razaviyayn , Vahab Mirrokni

Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower bounds for linear data structures would imply new bounds for rigid matrices. However, their result utilizes an algorithm that requires an $NP$ oracle, and…

Computational Complexity · Computer Science 2019-10-29 Sivaramakrishnan Natarajan Ramamoorthy , Cyrus Rashtchian

An integer polynomial $p$ of $n$ variables is called a \emph{threshold gate} for a Boolean function $f$ of $n$ variables if for all $x \in \zoon$ $f(x)=1$ if and only if $p(x)\geq 0$. The \emph{weight} of a threshold gate is the sum of its…

Computational Complexity · Computer Science 2015-07-01 Vladimir V. Podolskii

The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…

Information Theory · Computer Science 2022-05-04 Wenjing Chen , Chao Tian

We study the quantum query complexity of two problems. First, we consider the problem of determining if a sequence of parentheses is a properly balanced one (a Dyck word), with a depth of at most $k$. We call this the $Dyck_{k,n}$ problem.…

We consider a range-search variant of the closest-pair problem. Let $\varGamma$ be a fixed shape in the plane. We are interested in storing a given set of $n$ points in the plane in some data structure such that for any specified translate…

Computational Geometry · Computer Science 2019-03-25 Jie Xue , Yuan Li , Saladi Rahul , Ravi Janardan

In the dynamic set cover (SC) problem, the input is a dynamic universe of at most $n$ elements and a fixed collection of $m$ sets, where each element belongs to at most $f$ sets and each set has cost in $[1/C, 1]$. The objective is to…

Data Structures and Algorithms · Computer Science 2025-11-11 Shay Solomon , Amitai Uzrad

We study the problem of supporting queries on a string $S$ of length $n$ within a space bounded by the size $\gamma$ of a string attractor for $S$. Recent works showed that random access on $S$ can be supported in optimal…

Data Structures and Algorithms · Computer Science 2018-12-24 Nicola Prezza

We strengthen the connections between electrical transformations and homotopy from the planar setting---observed and studied since Steinitz---to arbitrary surfaces with punctures. As a result, we improve our earlier lower bound on the…

Computational Geometry · Computer Science 2019-03-27 Hsien-Chih Chang , Marcos Cossarini , Jeff Erickson

The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Theta(n^{1/5}) on the number of queries needed by a quantum computer to…

Quantum Physics · Physics 2007-05-23 Scott Aaronson

We prove a lower bound of $\tilde{\Omega}(n^{1/3})$ for the query complexity of any two-sided and adaptive algorithm that tests whether an unknown Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is monotone or far from monotone. This…

Computational Complexity · Computer Science 2017-08-22 Xi Chen , Erik Waingarten , Jinyu Xie