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 >>>

In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution $D$ over $[n]$. More precisely, we define both the dual and extended ... more >>>

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 >>>

A discrete distribution $p$, over $[n]$, is a $k$-histogram if its probability distribution function can be
represented as a piece-wise constant function with $k$ pieces. Such a function
is
represented by a list of $k$ intervals and $k$ corresponding values. We consider
the following problem: given a collection of samples ... more >>>

Sublinear time algorithms represent a new paradigm
in computing, where an algorithm must give some sort
of an answer after inspecting only a very small portion
of the input. We discuss the types of answers that
one can hope to achieve in this setting.

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 >>>

We investigate the number of samples required for testing the monotonicity of a distribution with respect to an arbitrary underlying partially ordered set. Our first result is a nearly linear lower bound for the sample complexity of testing monotonicity with respect to the poset consisting of a directed perfect matching. ... more >>>