arXiv subjects

Shai Gul

Publications and source records attributed to Shai Gul.

4 recordsLinked to original sources

arXiv2021

Efficient covering of convex domains by congruent discs

In this paper, we consider the problem of covering a plane region with unit discs. We present an improved upper bound and the first nontrivial lower bound on the number of discs needed for such a covering, depending on the area and perimeter of the region. We provide algorithms for efficient covering of convex polygonal regions using unit discs. We show that the computational complexity of the algorithms is pseudo-polynomial in the size of the input and the output. We also show that these algorithms provide a constant factor approximation of the optimal covering of the region.

cs.CG↗

arXiv2021

Online exploration outside a convex obstacle

A watchman path is a path such that a direct line of sight exists between each point in some region and some point along the path. Here, we study the online watchman path problem outside a convex polygon, i.e., in $\mathbb{R}^2\setminus Ω$, where $Ω$ is a convex polygon that is not known in advance. We present an algorithm for the exploration of the region outside the polygon. We prove that the presented algorithms guarantees a $\approx 22.77$ competitive ratio compared to the optimal offline watchman path.

cs.CG↗

arXiv2010

Creating Limit Functions By The Pang-Zalcman Lemma

In this paper we calculate the collection of limit functions obtained by applying an extension of Zalcman's Lemma, due to X. C. Pang, to the non-normal family $\left\{f(nz):n\in\mathbb{N}\right\}$ in $\mathbb{C}$, where $f=Re^P$. Here $R$ and $P$ are an arbitrary rational function and a polynomial, respectively, where $P$ is a non-constant polnomial.

math.CV↗

arXiv2010

$Q_α$-Normal Families and entire functions

For every countable ordinal number $α$ we construct an entire function $f=f_α$ such that the family $\left\{f(nz):n\in\mathbb{N}\right\}$ is exactly $Q_α$-normal in the unit disk.

math.CV↗