Michal Parnas, Dana Ron

We consider the problem of estimating the size, $VC(G)$, of a

minimum vertex cover of a graph $G$, in sublinear time,

by querying the incidence relation of the graph. We say that

an algorithm is an $(\alpha,\eps)$-approximation algorithm

if it outputs with high probability an estimate $\widehat{VC}$

such that ...
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Sofya Raskhodnikova, Dana Ron, Ronitt Rubinfeld, Amir Shpilka, Adam Smith

We raise the question of approximating compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and Lempel-Ziv (LZ), and present algorithms and lower bounds for approximating compressibility with respect to ... more >>>

Eldar Fischer, Orly Yahalom

A coloring of a graph is {\it convex} if it

induces a partition of the vertices into connected subgraphs.

Besides being an interesting property from a theoretical point of

view, tests for convexity have applications in various areas

involving large graphs. Our results concern the important subcase

of testing for ...
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Sofya Raskhodnikova, Adam Smith

We show that in the bounded degree model for graph property testing,

adaptivity is essential. An algorithm is *non-adaptive* if it makes all queries to the input before receiving any answers. We call a property *non-trivial* if it does not depend only on the degree distribution of the nodes. We ...
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Gregory Valiant, Paul Valiant

We introduce a new approach to characterizing the unobserved portion of a distribution, which provides sublinear-sample additive estimators for a class of properties that includes entropy and distribution support size. Together with the lower bounds proven in the companion paper [29], this settles the longstanding question of the sample complexities ... more >>>

Scott Aaronson, Andris Ambainis

We achieve essentially the largest possible separation between quantum and classical query complexities. We do so using a property-testing problem called Forrelation, where one needs to decide whether one Boolean function is highly correlated with the Fourier transform of a second function. This problem can be solved using 1 quantum ... more >>>

Jayadev Acharya, Clement Canonne, Gautam Kamath

A recent model for property testing of probability distributions enables tremendous savings in the sample complexity of testing algorithms, by allowing them to condition the sampling on subsets of the domain.

In particular, Canonne et al. showed that, in this setting, testing identity of an unknown distribution $D$ (i.e., ...
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Lucas Boczkowski, Iordanis Kerenidis, Frederic Magniez

We define the Streaming Communication model that combines the main aspects of communication complexity and streaming. We consider two agents that want to compute some function that depends on inputs that are distributed to each agent. The inputs arrive as data streams and each agent has a bounded memory. Agents ... more >>>

Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, Nithin Varma

We investigate the parameters in terms of which the complexity of sublinear-time algorithms should be expressed. Our goal is to find input parameters that are tailored to the combinatorics of the specific problem being studied and design algorithms that run faster when these parameters are small. This direction enables us ... more >>>