Jonas Holmerin

We prove that Minimum vertex cover on 4-regular hyper-graphs (or

in other words, hitting set where all sets have size exactly 4),

is hard to approximate within 2 - \epsilon.

We also prove that the maximization version, in which we

are allowed to pick ...
more >>>

Irit Dinur, Venkatesan Guruswami, Subhash Khot

Given a $k$-uniform hypergraph, the E$k$-Vertex-Cover problem is

to find a minimum subset of vertices that ``hits'' every edge. We

show that for every integer $k \geq 5$, E$k$-Vertex-Cover is

NP-hard to approximate within a factor of $(k-3-\epsilon)$, for

an arbitrarily small constant $\epsilon > 0$.

This almost matches the ... more >>>

Henning Fernau

In this paper, we show how to systematically

improve on parameterized algorithms and their

analysis, focusing on search-tree based algorithms

for d-Hitting Set, especially for d=3.

We concentrate on algorithms which are easy to implement,

in contrast with the highly sophisticated algorithms

which have been elsewhere designed to ...
more >>>

Henning Fernau

We are going to analyze simple search tree algorithms

for Weighted d-Hitting Set. Although the algorithms are simple, their analysis is technically rather involved. However, this approach allows us to even improve on elsewhere published algorithm running time estimates for the more restricted case of (unweighted) d-Hitting Set.

Venkatesan Guruswami, Yuan Zhou

We study the approximability of two natural Boolean constraint satisfaction problems: Horn satisfiability and exact hitting set. Under the Unique Games conjecture, we prove the following optimal inapproximability and approximability results for finding an assignment satisfying as many constraints as possible given a {\em

near-satisfiable} instance.

\begin{enumerate}

\item ...
more >>>

Jiri Sima, Stanislav Zak

The relationship between deterministic and probabilistic computations is one of the central issues in complexity theory. This problem can be tackled by constructing polynomial time hitting set generators which, however, belongs to the hardest problems in computer science even for severely restricted computational models. In our work, we consider read-once ... more >>>

Louay Bazzi, Nagi Nahas

Small-bias probability spaces have wide applications in pseudorandomness which naturally leads to the study of their limitations. Constructing a polynomial complexity hitting set for read-once CNF formulas is a basic open problem in pseudorandomness. We show in this paper that this goal is not achievable using small-bias spaces. Namely, we ... more >>>

Nader Bshouty

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 >>>

Venkatesan Guruswami, Euiwoong Lee

The {\em Unique Coverage} problem, given a universe $V$ of elements and a collection $E$ of subsets of $V$, asks to find $S \subseteq V$ to maximize the number of $e \in E$ that intersects $S$ in {\em exactly one} element. When each $e \in E$ has cardinality at most ... more >>>

Michael Forbes, Sumanta Ghosh, Nitin Saxena

Derandomization of blackbox identity testing reduces to extremely special circuit models. After a line of work, it is known that focusing on circuits with constant-depth and constantly many variables is enough (Agrawal,Ghosh,Saxena, STOC'18) to get to general hitting-sets and circuit lower bounds. This inspires us to study circuits with few ... more >>>

William Hoza, David Zuckerman

We give a simple explicit hitting set generator for read-once branching programs of width $w$ and length $r$ with known variable order. Our generator has seed length $O\left(\frac{\log(wr) \log r}{\max\{1, \log \log w - \log \log r\}} + \log(1/\varepsilon)\right)$. This seed length improves on recent work by Braverman, Cohen, and ... more >>>

Max Bannach, Zacharias Heinrich, RĂ¼diger Reischuk, Till Tantau

Computing kernels for the hitting set problem (the problem of

finding a size-$k$ set that intersects each hyperedge of a

hypergraph) is a well-studied computational problem. For hypergraphs

with $m$ hyperedges, each of size at most~$d$, the best algorithms

can compute kernels of size $O(k^d)$ in ...
more >>>

Kuan Cheng, William Hoza

A hitting set is a "one-sided" variant of a pseudorandom generator (PRG), naturally suited to derandomizing algorithms that have one-sided error. We study the problem of using a given hitting set to derandomize algorithms that have two-sided error, focusing on space-bounded algorithms. For our first result, we show that if ... more >>>

Pranjal Dutta, Nitin Saxena, Thomas Thierauf

We consider the univariate polynomial $f_d:=(x+1)^d$ when represented as a sum of constant-powers of univariate polynomials. We define a natural measure for the model, the support-union, and conjecture that it is $\Omega(d)$ for $f_d$.

We show a stunning connection of the conjecture to the two main problems in algebraic ... more >>>

Vishwas Bhargava, Sumanta Ghosh

The orbit of an $n$-variate polynomial $f(\mathbf{x})$ over a field $\mathbb{F}$ is the set $\{f(A \mathbf{x} + b)\,\mid\, A\in \mathrm{GL}({n,\mathbb{F}})\mbox{ and }\mathbf{b} \in \mathbb{F}^n\}$, and the orbit of a polynomial class is the union of orbits of all the polynomials in it. In this paper, we give improved constructions of ... more >>>