Related papers: Continuous Terrain Guarding with Two-Sided Guards
We address the persistent monitoring problem in two-dimensional mission spaces where the objective is to control the trajectories of multiple cooperating agents to minimize an uncertainty metric. In a one-dimensional mission space, we have…
Robotic access monitoring of multiple target areas has applications including checkpoint enforcement, surveillance and containment of fire and flood hazards. Monitoring access for a single target region has been successfully modeled as a…
This work concerns with the following problem. Given a two-dimensional domain whose boundary is a closed polygonal line with internal boundaries defined also by polygonal lines, it is required to generate a grid consisting only of…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More generally, we can consider the problem of finding (if possible) two points in $A$ and $B$,…
We consider the following variant of the two dimensional gathering problem for swarms of robots: Given a swarm of $n$ indistinguishable, point shaped robots on a two dimensional grid. Initially, the robots form a closed chain on the grid…
An important task in terrain analysis is computing \emph{viewsheds}. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly…
The strong geodetic problem is to find the smallest number of vertices such that by fixing one shortest path between each pair, all vertices of the graph are covered. In this paper we study the strong geodetic problem on complete bipartite…
We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$…
We address a problem of area protection in graph-based scenarios with multiple mobile agents where connectivity is maintained among agents to ensure they can communicate. The problem consists of two adversarial teams of agents that move in…
In computer games, traditional procedural terrain generation relies on a grid of vertices, with each point representing terrain elevation. For each square in the grid, two triangles are created by connecting fixed vertex indices, resulting…
This paper investigates the pursuit-evasion problem of a defensive gun turret and one or more attacking drones. The turret must ``visit" each attacking drone once, as quickly as possible, to defeat the threat. This constitutes a Shortest…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
We tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra.
In a given 2D space, we can have points with different levels of importance. One would prefer viewing those points from a closer/farther position per their level of importance. A point in 2D from where the user can view two given points per…
Critical point tracking is a core topic in scientific visualization for understanding the dynamic behavior of time-varying vector field data. The topological notion of robustness has been introduced recently to quantify the structural…
This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing…
We give a simple approximation algorithm for a common generalization of many previously studied extensions of the maximum size stable matching problem with ties. These generalizations include the existence of critical vertices in the graph,…
Recently, object detection has proven vulnerable to adversarial patch attacks. The attackers holding a specially crafted patch can hide themselves from state-of-the-art detectors, e.g., YOLO, even in the physical world. This attack can…
We study several variations of line segment covering problem with axis-parallel unit squares in $I\!\!R^2$. A set $S$ of $n$ line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at…