In this work we consider the problem of approximating the number of relevant variables in a function given query access to the function. Since obtaining a multiplicative factor approximation is hard in general, we consider several relaxations of the problem. In particular, we consider relaxations in which we have a ... more >>>

Property testing is concerned with deciding whether an object
(e.g. a graph or a function) has a certain property or is ``far''
(for a prespecified distance measure) from every object with
that property. In this work we consider the property of being
computable by a read-once ... more >>>

We propose a framework for studying property testing of collections of distributions,
where the number of distributions in the collection is a parameter of the problem.
Previous work on property testing of distributions considered
single distributions or pairs of distributions. We suggest two models that differ
in the way the ... more >>>

Detecting and counting the number of copies of certain subgraphs (also known as {\em network motifs\/} or {\em graphlets\/}), is motivated by applications in a variety of areas ranging from Biology to the study of the World-Wide-Web. Several polynomial-time algorithms have been suggested for counting or detecting the number of ... more >>>

We initiate a systematic study of a special type of property testers.
These testers consist of repeating a basic test
for a number of times that depends on the proximity parameters,
whereas the basic test is oblivious of the proximity parameter.
We refer to such basic tests ... more >>>

In this paper we consider two refined questions regarding
the query complexity of testing graph properties
in the adjacency matrix model.
The first question refers to the relation between adaptive
and non-adaptive testers, whereas the second question refers to
testability within complexity that
is inversely proportional to ... more >>>

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 >>>

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 ... more >>>

Inspired by Feige ({\em 36th STOC}, 2004),
we initiate a study of sublinear randomized algorithms
for approximating average parameters of a graph.
Specifically, we consider the average degree of a graph
and the average distance between pairs of vertices in a graph.
Since our focus is on sublinear algorithms, these ... more >>>

Following Feige, we consider the problem of
estimating the average degree of a graph.
Using ``neighbor queries'' as well as ``degree queries'',
we show that the average degree can be approximated
arbitrarily well in sublinear time, unless the graph is extremely sparse
(e.g., unless the graph has a sublinear ... more >>>

A standard property testing algorithm is required to determine
with high probability whether a given object has property
P or whether it is \epsilon-far from having P, for any given
distance parameter \epsilon. An object is said to be \epsilon-far
from having property P if ... more >>>

Traditionally, communication networks are composed of
routing nodes, which relay and duplicate data. Work in
recent years has shown that for the case of multicast, an
improvement in both rate and code-construction complexity can be
gained by replacing these routing nodes by linear coding
nodes. These nodes transmit linear combinations ... more >>>

We consider the problem of determining whether a given
function f : {0,1}^n -> {0,1} belongs to a certain class
of Boolean functions F or whether it is far from the class.
More precisely, given query access to the function f and given
a distance parameter epsilon, we would ... more >>>

We consider testing graph expansion in the bounded-degree graph model.
Specifically, we refer to algorithms for testing whether the graph
has a second eigenvalue bounded above by a given threshold
or is far from any graph with such (or related) property.

We present a natural algorithm aimed towards ... more >>>

We present improved algorithms for testing monotonicity of functions.
Namely, given the ability to query an unknown function $f$, where
$\Sigma$ and $\Xi$ are finite ordered sets, the test always accepts a
monotone $f$, and rejects $f$ with high probability if it is $\e$-far
from being monotone (i.e., every monotone ... more >>>

The Chinese Remainder Theorem states that a positive
integer m is uniquely specified by its remainder modulo
k relatively prime integers p_1,...,p_k, provided
m < \prod_{i=1}^k p_i. Thus the residues of m modulo
relatively prime integers p_1 < p_2 < ... < p_n
form a redundant representation of m if ... more >>>

In a variety of PAC learning models, a tradeoff between time and
information seems to exist: with unlimited time, a small amount of
information suffices, but with time restrictions, more information
sometimes seems to be required.
In addition, it has long been known that there are
concept classes that ... more >>>

In this paper, we consider the question of determining whether
a function $f$ has property $P$ or is $\e$-far from any
function with property $P$.
The property testing algorithm is given a sample of the value
of $f$ on instances drawn according to some distribution.
In some cases,
it ... more >>>