We prove that to estimate within a constant factor the number of defective items in a non-adaptive group testing algorithm we need at least $\tilde\Omega((\log n)(\log(1/\delta)))$ tests. This solves the open problem posed by Damaschke and Sheikh Muhammad.

Derandomization of Chernoff bound with union bound is already proven in many papers.
We here give another explicit version of it that obtains a construction of size
that is arbitrary close to the probabilistic nonconstructive size.

We apply this to give a new simple polynomial time constructions of
almost $k$-wise ... more >>>

We develop a new notion called {\it $(1-\epsilon)$-tester for a
set $M$ of functions} $f:A\to C$. A $(1-\epsilon)$-tester
for $M$ maps each element $a\in A$ to a finite number of
elements $B_a=\{b_1,\ldots,b_t\}\subset B$ in a smaller
sub-domain $B\subset A$ where for every $f\in M$ if
$f(a)\not=0$ then $f(b)\not=0$ for at ... more >>>

We develop a new algebraic technique that gives a simple randomized algorithm for the simple $k$-path problem with the same complexity $O^*(1.657^k)$ as in [A. Bj\"orklund. Determinant Sums for Undirected Hamiltonicity. FOCS 2010, pp. 173--182, (2010). A. Bj\"orklund, T. Husfeldt, P. Kaski, M. Koivisto. Narrow sieves for parameterized paths and ... more >>>

In this paper we first show that Tester for an $F$-algebra $A$
and multilinear forms (see Testers and their Applications ECCC 2012) is equivalent to multilinear
algorithm for the product of elements in $A$
(see Algebraic
complexity theory. vol. 315, Springer-Verlag). Our
result is constructive in deterministic polynomial time. ... more >>>

We develop a new notion called {\it tester of a class $\cM$ of
functions} $f:\cA\to \cC$ that maps the elements $\bfa\in \cA$ in
the domain $\cA$ of the function to a finite number (the size of
the tester) of elements $\bfb_1,\ldots,\bfb_t$ in a smaller
sub-domain $\cB\subset \cA$ where the property ... more >>>

The coin weighing problem is the following: Given $n$ coins for which $m$ of them are counterfeit with the same weight. The problem is to detect the counterfeit coins with minimal number of weighings. This problem has many applications in compressed sensing, multiple access adder channels, etc. The problem was ... more >>>