Related papers: Improved Algorithms for Minimum-Membership Geometr…
We revisit a natural variant of geometric set cover, called minimum-membership geometric set cover (MMGSC). In this problem, the input consists of a set $S$ of points and a set $\mathcal{R}$ of geometric objects, and the goal is to find a…
We study the minimum membership geometric set cover, i.e., MMGSC problem [SoCG, 2023] in the continuous setting. In this problem, the input consists of a set $P$ of $n$ points in $\mathbb{R}^{2}$, and a geometric object $t$, the goal is to…
We provide a comprehensive study of a natural geometric optimization problem motivated by questions in the context of satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs (MSC), we are given a graph…
We study the generalized min sum set cover (GMSSC) problem, wherein given a collection of hyperedges $E$ with arbitrary covering requirements $k_e$, the goal is to find an ordering of the vertices to minimize the total cover time of the…
Biedl et al. introduced the minimum ply cover problem in CG 2021 following the seminal work of Erlebach and van Leeuwen in SODA 2008. They showed that determining the minimum ply cover number for a given set of points by a given set of…
We study the \emph{generalized min-sum set cover} (GMSSC) problem, where given a collection of hyperedges $E$ with arbitrary covering requirements $\{k_e \in \mathbb{Z}^+ : e \in E\}$, the objective is to find an ordering of the vertices…
Following the seminal work of Erlebach and van Leeuwen in SODA 2008, we introduce the minimum ply covering problem. Given a set $P$ of points and a set $S$ of geometric objects, both in the plane, our goal is to find a subset $S'$ of $S$…
Subgraph complementation is an operation that toggles all adjacencies inside a selected vertex set. Given a graph \(G\) and a target class \(\mathcal{C}\), the Minimum Subgraph Complementation problem asks for a minimum-size vertex set…
In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of…
We study the minimum vertex cover problem in the following stochastic setting. Let $G$ be an arbitrary given graph, $p \in (0, 1]$ a parameter of the problem, and let $G_p$ be a random subgraph that includes each edge of $G$ independently…
Given a set $P$ of points and a set $U$ of axis-parallel unit squares in the Euclidean plane, a minimum ply cover of $P$ with $U$ is a subset of $U$ that covers $P$ and minimizes the number of squares that share a common intersection,…
We study the minimum \emph{Monitoring Edge Geodetic Set} (\megset) problem introduced in [Foucaud et al., CALDAM'23]: given a graph $G$, we say that an edge is monitored by a pair $u,v$ of vertices if \emph{all} shortest paths between $u$…
Partial Set Cover (PSC) is a generalization of the well-studied Set Cover problem (SC). In PSC the input consists of an integer $k$ and a set system $(U,S)$ where $U$ is a finite set, and $S \subseteq 2^U$ is a collection of subsets of $U$.…
We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs, we are given a graph $G$ that is embedded in Euclidean…
Consider a sliding camera that travels back and forth along an orthogonal line segment $s$ inside an orthogonal polygon $P$ with $n$ vertices. The camera can see a point $p$ inside $P$ if and only if there exists a line segment containing…
We study the complexity of finding the \emph{geodetic number} on subclasses of planar graphs and chordal graphs. A set $S$ of vertices of a graph $G$ is a \emph{geodetic set} if every vertex of $G$ lies in a shortest path between some pair…
Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…
We study the Minimum Latency Submodular Cover problem (MLSC), which consists of a metric $(V,d)$ with source $r\in V$ and $m$ monotone submodular functions $f_1, f_2, ..., f_m: 2^V \rightarrow [0,1]$. The goal is to find a path originating…
We introduce a parameterized version of set cover that generalizes several previously studied problems. Given a ground set V and a collection of subsets S_i of V, a feasible solution is a partition of V such that each subset of the…
We consider the set multi-cover problem in geometric settings. Given a set of points P and a collection of geometric shapes (or sets) F, we wish to find a minimum cardinality subset of F such that each point p in P is covered by (contained…