# Questions tagged [property-testing]

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### How long does it take to find a short cycle in a random graph?

Let $G \sim G(n, n^{-1/2})$ be a random graph on $\approx n^{3/2}$ edges. With very high probability, $G$ has many $4$-cycles. Our goal is to output any one of these $4$-cycles as quickly as ...
182 views

### Generalization of Element Distinctness

In the element distinctness problem, one has query access to an arbitrary multiset of $n$ elements and must decide whether they are all distinct. From a property testing point of view, the question ...
87 views

### Robustness to non-uniform randomness vs. one-sidedness

Consider any problem where, fixing two (disjoint) subsets $\mathcal{Y},\mathcal{N}\subseteq \{0,1\}^n$ of the input space, the goal is to obtain a randomized algorithm $D$ which, given a uniformly ...
184 views

### Distinguishing a biased coin with a small set of tests

Say we have a "coin" $f : [n] \to \{\pm 1\}$ so that either $f$ is balanced, or $f$ is $\epsilon$-far from being balanced. It's a classic result that sampling $O(1/\epsilon^2)$ random points of $f$ ...
149 views

132 views

### Testing low degree bivariate polynomials

Let $d,q \in \mathbb{N}$, and let $f:\mathrm{GF}(q) \to \mathrm{GF}(q)$ be a univariate polynomial. In this case, it is possible to test whether $f$ is of degree at most $d$ (or whether $f$ is at ...
In graph property testing, an algorithm queries a target graph for the presence or absence of edges and needs to determine whether the target either has a certain property or is $\epsilon$-far from ...