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Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However,…

Artificial Intelligence · Computer Science 2025-02-19 Damiano Azzolini , Fabrizio Riguzzi

The $K$-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of $n$ data points with labels and a query point $p$, we want to assign a label to $p$ based on the labels…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-25 Reza Fathi , Anisur Rahaman Molla , Gopal Pandurangan

Given a $k$-uniform hyper-graph, the E$k$-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to…

Computational Complexity · Computer Science 2007-05-23 Irit Dinur , Venkatesan Guruswami , Subhash Khot , Oded Regev

We study the problem of computing the $p\rightarrow q$ norm of a matrix $A \in R^{m \times n}$, defined as \[ \|A\|_{p\rightarrow q} ~:=~ \max_{x \,\in\, R^n \setminus \{0\}} \frac{\|Ax\|_q}{\|x\|_p} \] This problem generalizes the spectral…

Computational Complexity · Computer Science 2018-08-10 Vijay Bhattiprolu , Mrinalkanti Ghosh , Venkatesan Guruswami , Euiwoong Lee , Madhur Tulsiani

We present a new type of monotone submodular functions: \emph{multi-peak submodular functions}. Roughly speaking, given a family of sets $\cF$, we construct a monotone submodular function $f$ with a high value $f(S)$ for every set $S \in…

Data Structures and Algorithms · Computer Science 2015-03-20 Shahar Dobzinski , Jan Vondrak

We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…

Data Structures and Algorithms · Computer Science 2016-01-22 Clément L. Canonne , Ilias Diakonikolas , Themis Gouleakis , Ronitt Rubinfeld

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics over the past three decades. Recently, they have found applications in theoretical computer science, including to proving…

Computational Complexity · Computer Science 2020-09-11 Mohammad Mahdi Jahanara , Sajin Koroth , Igor Shinkar

We establish new hardness results for decision tree optimization problems, adding to a line of work that dates back to Hyafil and Rivest in 1976. We prove, under randomized ETH, superpolynomial lower bounds for two basic problems: given an…

Computational Complexity · Computer Science 2022-10-13 Caleb Koch , Carmen Strassle , Li-Yang Tan

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

Data Structures and Algorithms · Computer Science 2008-10-29 Marek Cygan , Lukasz Kowalik , Marcin Pilipczuk , Mateusz Wykurz

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

Information Theory · Computer Science 2008-06-09 Michael Chertkov , Lukas Kroc , Massimo Vergassola

Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…

Data Structures and Algorithms · Computer Science 2025-10-17 Noah Fleming , Yuichi Yoshida

The \emph{Steiner tree} problem is one of the fundamental and classical problems in combinatorial optimization. In this paper, we study this problem in the $\mathcal{CONGESTED}$ $\mathcal{CLIQUE}$ model of distributed computing and present…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-31 Parikshit Saikia , Sushanta Karmakar

We observe an infinite sequence of independent identically distributed random variables $X_1,X_2,\ldots$ drawn from an unknown distribution $p$ over $[n]$, and our goal is to estimate the entropy $H(p)=-\mathbb{E}[\log p(X)]$ within an…

Information Theory · Computer Science 2025-04-24 Tomer Berg , Or Ordentlich , Ofer Shayevitz

In pursuit of a deeper understanding of Boolean Promise Constraint Satisfaction Problems (PCSPs), we identify a class of problems with restricted structural complexity, which could serve as a promising candidate for complete…

Computational Complexity · Computer Science 2025-10-01 Katzper Michno

Some of the most fundamental and well-studied graph parameters are the Diameter (the largest shortest paths distance) and Radius (the smallest distance for which a "center" node can reach all other nodes). The natural and important…

Data Structures and Algorithms · Computer Science 2019-04-29 Mina Dalirrooyfard , Virginia Vassilevska Williams , Nikhil Vyas , Nicole Wein

The objective of generative model inversion is to identify a size-$n$ latent vector that produces a generative model output that closely matches a given target. This operation is a core computational primitive in numerous modern…

Machine Learning · Statistics 2023-09-13 Feyza Duman Keles , Chinmay Hegde

We consider the task of distributed inner product estimation when allowed limited quantum communication. Here, Alice and Bob are given $k$ copies of an unknown $n$-qubit quantum states $\vert \psi \rangle,\vert \phi \rangle$ respectively.…

Quantum Physics · Physics 2024-10-17 Srinivasan Arunachalam , Louis Schatzki

We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory $\mathrm{APC}_2$ of…

Logic · Mathematics 2021-11-29 Leszek Aleksander Kołodziejczyk , Neil Thapen

In CPM 2017, Amir et al. introduce a problem, named \emph{approximate string cover} (\textbf{ACP}), motivated by many aplications including coding and automata theory, formal language theory, combinatorics and molecular biology. A…

Data Structures and Algorithms · Computer Science 2018-06-22 Alexandru Popa , Andrei Tanasescu

Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-05 Adar Hadad , Moni Naor