Related papers: Classifying Identities: Subcubic Distributivity Ch…
We study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and…
As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify…
Whittle index is a generalization of Gittins index that provides very efficient allocation rules for restless multi-armed bandits. In this work, we develop an algorithm to test the indexability and compute the Whittle indices of any…
Identifying symmetries in quantum dynamics, such as identity or time-reversal invariance, is a crucial challenge with profound implications for quantum technologies. We introduce a unified framework combining group representation theory and…
In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…
A recent model for property testing of probability distributions (Chakraborty et al., ITCS 2013, Canonne et al., SICOMP 2015) enables tremendous savings in the sample complexity of testing algorithms, by allowing them to condition the…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
We consider the problem of exact identification for read-once functions over arbitrary Boolean bases. We introduce a new type of queries (subcube identity ones), discuss its connection to previously known ones, and study the complexity of…
The possibilities offered by quantum computing have drawn attention in the distributed computing community recently, with several breakthrough results showing quantum distributed algorithms that run faster than the fastest known classical…
We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
Many problems in interprocedural program analysis can be modeled as the context-free language (CFL) reachability problem on graphs and can be solved in cubic time. Despite years of efforts, there are no known truly sub-cubic algorithms for…
Samplers are the backbone of the implementations of any randomised algorithm. Unfortunately, obtaining an efficient algorithm to test the correctness of samplers is very hard to find. Recently, in a series of works, testers like…
Solitude verification is arguably one of the simplest fundamental problems in distributed computing, where the goal is to verify that there is a unique contender in a network. This paper devises a quantum algorithm that exactly solves the…
Proving linear inequalities and identities of Shannon's information measures, possibly with linear constraints on the information measures, is an important problem in information theory. For this purpose, ITIP and other variant algorithms…
We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated $2^{O(\sqrt{\log n})}$-time algorithm of Panconesi and Srinivasan [STOC'92] and settles a central and…
Motivated by an open direction in existing literature, we study the 1-identification problem, a fundamental multi-armed bandit formulation on pure exploration. The goal is to determine whether there exists an arm whose mean reward is at…
Modal parameter estimation of operational structures is often a challenging task when confronted with unwanted distortions (outliers) in field measurements. Atypical observations present a problem to operational modal analysis (OMA)…
We study property testing in the subcube conditional model introduced by Bhattacharyya and Chakraborty (2017). We obtain the first equivalence test for $n$-dimensional distributions that is quasi-linear in $n$, improving the previously…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…