Related papers: Contiguous Boundary Guarding
Victor Klee introduce the art gallery problem during a conference in Stanford in August 1976 with that question: "How many guards are required to guard an art gallery?" In 1987, Ghosh provided an approximation algorithm for vertex guards…
The contiguous art gallery problem was introduced at SoCG'25 in a merged paper that combined three simultaneous results, each achieving a polynomial-time algorithm for the problem. This problem is a variant of the classical art gallery…
We prove that every simply connected orthogonal polygon of $n$ vertices can be partitioned into $\left\lfloor\frac{3 n +4}{16}\right\rfloor$ (simply connected) orthogonal polygons of at most 8 vertices. It yields a new and shorter proof of…
Given a simple polygon $\cal P$, in the Art Gallery problem, the goal is to find the minimum number of guards needed to cover the entire $\cal P$, where a guard is a point and can see another point $q$ when $\overline{pq}$ does not cross…
We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…
Art Gallery is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P, (possibly infinite) sets G and C of points within P, and an integer k; the task is to decide if at most k guards can be…
This paper addresses the problem of tracking mobile intruders in a polygonal environment. We assume that a team of diagonal guards is deployed inside the polygon to provide mobile coverage. First, we formulate the problem of tracking a…
We present two new versions of the chromatic art gallery problem that can improve upper bound of the required colors pretty well. In our version, we employ restricted angle guards so that these modern guards can visit $\alpha$-degree of…
This paper focuses on a variation of the Art Gallery problem that considers open edge guards and open mobile guards. A mobile guard can be placed on edges and diagonals of a polygon, and the "open" prefix means that the endpoints of such…
We study the problem of Covering Orthogonal Polygons with Rectangles. For polynomial-time algorithms, the best-known approximation factor is $O(\sqrt{\log n})$ when the input polygon may have holes [Kumar and Ramesh, STOC '99, SICOMP '03],…
We perform structural and algorithmic studies of significantly generalized versions of the optimal perimeter guarding (OPG) problem. As compared with the original OPG where robots are uniform, in this paper, many mobile robots with…
Given an $x$-monotone polygonal chain $T$ with $n$ vertices, and an integer $k$, we consider the problem of finding the lowest horizontal line $L$ lying above $T$ with $k$ point guards lying on $L$, so that every point on the chain is…
We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using "rectangular vision". We prove a sharp bound on the minimum number of point guards required to cover…
We consider the problem of covering the boundary of a simple polygon on n vertices using the minimum number of geodesic unit disks. We present an O(n \log^2 n+k) time 2-approximation algorithm for finding the centers of the disks, with k…
The Art Gallery Problem (AGP) asks for placing a minimum number of stationary guards in a polygonal region P, such that all points in P are guarded. The problem is known to be NP-hard, and its inherent continuous structure (with both the…
Placing a minimum number of guards on a given watchman route in a polygonal domain is called the {\em minimum vision points problem}. We prove that finding the minimum number of vision points on a shortest watchman route in a simple polygon…
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational…
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…
We study a variant of the geometric multicut problem, where we are given a set $\mathcal{P}$ of colored and pairwise interior-disjoint polygons in the plane. The objective is to compute a set of simple closed polygon boundaries (fences)…
The Searchlight Scheduling Problem was first studied in 2D polygons, where the goal is for point guards in fixed positions to rotate searchlights to catch an evasive intruder. Here the problem is extended to 3D polyhedra, with the guards…