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Electronic Colloquium on Computational Complexity

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All reports by Author Dana Ron:

TR18-185 | 6th November 2018
Yonatan Nakar, Dana Ron

On the Testability of Graph Partition Properties

In this work we study the testability of a family of graph partition properties that generalizes a family previously studied by Goldreich, Goldwasser, and Ron (Journal of the ACM, 1998). While the family studied by Goldreich et al. includes a variety of natural properties, such as k-colorability and containing a ... more >>>

TR18-045 | 6th March 2018
Oded Goldreich, Dana Ron

The Subgraph Testing Model

We initiate a study of testing properties of graphs that are presented as subgraphs of a fixed (or an explicitly given) graph.
The tester is given free access to a base graph $G=([\n],E)$, and oracle access to a function $f:E\to\{0,1\}$ that represents a subgraph of $G$.
The tester is ... more >>>

TR16-105 | 13th July 2016
Eric Blais, Clement Canonne, Talya Eden, Amit Levi, Dana Ron

Tolerant Junta Testing and the Connection to Submodular Optimization and Function Isomorphism

Revisions: 1

The function $f\colon \{-1,1\}^n \to \{-1,1\}$ is a $k$-junta if it depends on at most $k$ of its variables. We consider the problem of tolerant testing of $k$-juntas, where the testing algorithm must accept any function that is $\epsilon$-close to some $k$-junta and reject any function that is $\epsilon'$-far from ... more >>>

TR15-046 | 2nd April 2015
Talya Eden, Amit Levi, Dana Ron

Approximately Counting Triangles in Sublinear Time

Comments: 1

We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in two models: Exact counting algorithms, which require reading the entire graph, and streaming algorithms, where the edges are given in a stream and the memory is limited. In this work ... more >>>

TR15-019 | 3rd February 2015
Reut Levi, Guy Moshkovitz, Dana Ron, Ronitt Rubinfeld, Asaf Shapira

Constructing Near Spanning Trees with Few Local Inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let $G$ be a connected bounded-degree graph. Given an edge $e$ in $G$ we would like ... more >>>

TR14-029 | 4th March 2014
Oded Goldreich, Dana Ron

On Learning and Testing Dynamic Environments

Revisions: 3

We initiate a study of learning and testing dynamic environments,
focusing on environment that evolve according to a fixed local rule.
The (proper) learning task consists of obtaining the initial configuration
of the environment, whereas for non-proper learning it suffices to predict
its future values. The testing task consists of ... more >>>

TR13-109 | 11th August 2013
Oded Goldreich, Dana Ron

On Sample-Based Testers

Revisions: 1

The standard definition of property testing endows the tester with the ability to make arbitrary queries to ``elements''
of the tested object.
In contrast, sample-based testers only obtain independently distributed elements (a.k.a. labeled samples) of the tested object.
While sample-based testers were defined by
Goldreich, Goldwasser, and Ron ({\em JACM}\/ ... more >>>

TR13-096 | 25th June 2013
Dana Ron, Rocco Servedio

Exponentially improved algorithms and lower bounds for testing signed majorities

A signed majority function is a linear threshold function $f : \{+1,1\}^n \to \{+1,1\}$ of the form
$f(x)={\rm sign}(\sum_{i=1}^n \sigma_i x_i)$ where each $\sigma_i \in \{+1,-1\}.$ Signed majority functions are a highly symmetrical subclass of the class of all linear threshold functions, which are functions of the form ${\rm ... more >>>

TR12-155 | 15th November 2012
Clement Canonne, Dana Ron, Rocco Servedio

Testing probability distributions using conditional samples

Revisions: 1

We study a new framework for property testing of probability distributions, by considering distribution testing algorithms that have access to a conditional sampling oracle. \footnote{Independently from our work, Chakraborty et al. [CFGM13] also considered this framework. We discuss their work in Subsection 1.4.} This is an oracle that takes as ... more >>>

TR12-101 | 10th August 2012
Oded Goldreich, Shafi Goldwasser, Dana Ron

On the possibilities and limitations of pseudodeterministic algorithms

We study the possibilities and limitations
of pseudodeterministic algorithms,
a notion put forward by Gat and Goldwasser (2011).
These are probabilistic algorithms that solve search problems
such that on each input, with high probability, they output
the same solution, which may be thought of as a canonical solution.
We consider ... more >>>

TR12-055 | 4th May 2012
Reut Levi, Dana Ron, Ronitt Rubinfeld

Testing Similar Means

We consider the problem of testing a basic property of collections of distributions: having similar means. Namely, the algorithm should accept collections of distributions in which all distributions have means that do not differ by more than some given parameter, and should reject collections that are relatively far from having ... more >>>

TR12-035 | 5th April 2012
Artur Czumaj, Oded Goldreich, Dana Ron, C. Seshadhri, Asaf Shapira, Christian Sohler

Finding Cycles and Trees in Sublinear Time

Revisions: 1 , Comments: 1

(This is a revised version of work that was posted on arXiv in July 2010.)

We present sublinear-time (randomized) algorithms for finding simple cycles of length at least $k\geq3$ and tree-minors in bounded-degree graphs.
The complexity of these algorithms is related to the distance
of the graph from being ... more >>>

TR11-078 | 9th May 2011
Dana Ron, Gilad Tsur

On Approximating the Number of Relevant Variables in a Function

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 >>>

TR11-041 | 24th March 2011
Dana Ron, Gilad Tsur

Testing Computability by Width-Two OBDDs

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 >>>

TR10-157 | 24th October 2010
Reut Levi, Dana Ron, Ronitt Rubinfeld

Testing Properties of Collections of Distributions

Revisions: 1

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 >>>

TR09-083 | 24th September 2009
Dana Ron, Mira Gonen, Yuval Shavitt

Counting Stars and Other Small Subgraphs in Sublinear Time

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 >>>

TR08-041 | 10th April 2008
Oded Goldreich, Dana Ron

On Proximity Oblivious Testing

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 ... more >>>

TR08-039 | 7th April 2008
Oded Goldreich, Dana Ron

Algorithmic Aspects of Property Testing in the Dense Graphs Model

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 >>>

TR05-125 | 2nd November 2005
Sofya Raskhodnikova, Dana Ron, Ronitt Rubinfeld, Amir Shpilka, Adam Smith

Sublinear Algorithms for Approximating String Compressibility and the Distribution Support Size

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 >>>

TR05-094 | 9th August 2005
Michal Parnas, Dana Ron

On Approximating the Minimum Vertex Cover in Sublinear Time and the Connection to Distributed Algorithms

Revisions: 1

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 >>>

TR05-073 | 14th July 2005
Oded Goldreich, Dana Ron

Approximating Average Parameters of Graphs.

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, ... more >>>

TR04-013 | 10th February 2004
Oded Goldreich, Dana Ron

On Estimating the Average Degree of a Graph.

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 >>>

TR04-010 | 26th January 2004
Michal Parnas, Dana Ron, Ronitt Rubinfeld

Tolerant Property Testing and Distance Approximation

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 ... more >>>

TR03-033 | 6th May 2003
Meir Feder, Dana Ron, Ami Tavory

Bounds on Linear Codes for Network Multicast

Comments: 1

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 >>>

TR01-063 | 5th August 2001
Michal Parnas, Dana Ron, Alex Samorodnitsky

Proclaiming Dictators and Juntas or Testing Boolean Formulae

Revisions: 1

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 >>>

TR00-020 | 27th March 2000
Oded Goldreich, Dana Ron

On Testing Expansion in Bounded-Degree Graphs

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 ... more >>>

TR99-017 | 4th June 1999
Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, Alex Samorodnitsky

Improved Testing Algorithms for Monotonicity.

Revisions: 1

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 ... more >>>

TR98-062 | 28th October 1998
Oded Goldreich, Dana Ron, Madhu Sudan

Chinese Remaindering with Errors

Revisions: 4 , Comments: 1

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 >>>

TR97-028 | 12th July 1997
Scott E. Decatur, Oded Goldreich, Dana Ron

Computational Sample Complexity

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 ... more >>>

TR96-057 | 18th November 1996
Oded Goldreich, Dana Ron

Property Testing and its connection to Learning and Approximation

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,
more >>>

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