arXiv subjects

Marzieh Eskandari

Publications and source records attributed to Marzieh Eskandari.

2 recordsLinked to original sources

arXiv2021

Lower Bound for Sculpture Garden Problem

The purpose of the current study is to investigate a special case of art gallery problem, namely Sculpture Garden Problem. In the said problem, for a given polygon $P$, the ultimate goal is to place the minimum number of guards to define the interior polygon $P$ by applying a monotone Boolean formula composed of the guards. As the findings indicate, the conjecture about the issue that in the worst case, $n-2$ guards are required to describe any $n$-gon (Eppstein et al. 2007) can be conclusively proved.

cs.CG↗

arXiv2021

Separated Red Blue Center Clustering

We study a generalization of $k$-center clustering, first introduced by Kavand et. al., where instead of one set of centers, we have two types of centers, $p$ red and $q$ blue, and where each red center is at least $α$ distant from each blue center. The goal is to minimize the covering radius. We provide an approximation algorithm for this problem, and a polynomial time algorithm for the constrained problem, where all the centers must lie on a line $\ell$.

cs.CG↗