Improved Bounds for Wireless Localization

We consider a novel class of art gallery problems inspired by wireless localization that has recently been introduced by Eppstein, Goodrich, and Sitchinava. Given a simple polygonP, place and orient guards each of which broadcasts a unique key within a fixed angular range. In contrast to the classical art gallery setting, broadcasts are not blocked by the edges ofP. At any point in the plane one must be able to tell whether or not one is located inside P only by looking at the set of keys received. In other words, the interior of the polygon must be described by a monotone Boolean formula composed from the keys. We improve both upper and lower bounds for the general problem where guards may be placed anywhere by showing that the maximum number of guards to describe any simple polygon on n vertices is between roughly $\frac{3}{5}n$ and $\frac{4}{5}n$ . Aguarding that uses at most $\frac{4}{5}n$ guards can be obtained in O(nlog n) time. For the natural setting where guards may be placed aligned to one edge or two consecutive edges ofP only, we prove that n−2 guards are always sufficient and sometimes necessar

Automatic construction, maintenance, and optimization of dynamic agent organizations

The goal of this dissertation is to generate organizational structures that increase the overall performance of a multiagent coalition, subject to the system's complex coordination requirements and maintenance of a certain operating point. To this end, a generalized framework capable of producing distributed approximation algorithms based on the new concept of multidirectional graph search is proposed and applied to a family of connectivity problems. It is shown that a wide variety of seemingly unrelated multiagent organization problems live within this family. Su cient conditions are identi ed in which the approach is guaranteed to discover a solution that is within a constant factor of the cost of the optimal solution. The procedure is guaranteed to require no more than linear|and in some well de ned cases logarithmic|communication rounds. A number of examples are given as to how the framework can be applied to create, maintain, and optimize multiagent organizations in the context of real world problems. Finally, algorithmic extensions are introduced that allow for the framework to handle problems in which the agent topology and/or coordination constraints are dynamic, without signi cant consequences to the general runtime, memory, and quality guarantees.Ph.D., Computer Science -- Drexel University, 201

AUTOMATED 3D CAMERA PLACEMENT

This project aims to find the minimum number of cameras needed to observe given three-dimensional (3D) environment and the cameras placement. This report traces the structure of the algorithm used to find the optimal number and placement of the cameras, the deployment of the algorithm in camera placement system, and presents the results of testing done on the system. This study related to the well known Art Gallery Problem (AGP) that addressed the problem of finding minimum number of guards necessary to guard the art gallery. Since this problem was posed, much research has been done on solving the problem from two dimensional (2D) perspectives. Not much research is done from 3D perspective and only recently more researchers are interested to study this problem in 3D environment.

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Maximizing the guarded boundary of an art gallery is APX-complete

In the Art Gallery problem, given is a polygonal gallery and the goal is to guard the gallery's interior or walls with a number of guards that must be placed strategically in the interior, on walls or on corners of the gallery. Here we consider a more realistic version: exhibits now have size and may have different costs. Moreover the meaning of guarding is relaxed: we use a new concept, that of watching an expensive art item, i.e. overseeing a part of the item. The main result of the paper is that the problem of maximizing the total value of a guarded weighted boundary is APX-complete. This is shown by an appropriate 'gap-preserving' reduction from the Max-5-occurrence-3-Sat problem. We also show that this technique can be applied to a number of maximization variations of the art gallery problem. In particular we consider the following problems: given a polygon with or without holes and k available guards, maximize a) the length of walls guarded and b) the total cost of paintings watched or overseen. We prove that all the above problems are APX-complete. © 2006 Elsevier B.V

Maximizing the Guarded Boundary of an Art Gallery is APX-complete ⋆

In the Art Gallery problem, given is a polygonal gallery and the goal is to guard the gallery’s interior or walls with a number of guards that must be placed strategically in the interior, on walls or on corners of the gallery. Here we consider a more realistic version: exhibits now have size and may have different costs. Moreover the meaning of guarding is relaxed: we use a new concept, that of watching an expensive art item, i.e. overseeing a part of the item. The main result of the paper is that the problem of maximizing the total value of a guarded weighted boundary is APX-complete. This is shown by an appropriate ‘gap-preserving ’ reduction from the Max-5-occurrence-3-Sat problem. We also show that this technique can be applied to a number of maximization variations of the art gallery problem. In particular we consider the following problems: given a polygon with or without holes and k available guards, maximize a) the length of walls guarded and b) the total cost of paintings watched or overseen. We prove that all the above problems are APX-complete

Maximizing the Guarded Boundary of an Art Gallery is APX-complete

In the Art Gallery problem, given is a polygonal gallery and the goal is to guard the gallery’s interior or walls with a number of guards that must be placed strategically in the interior, on walls or on corners of the gallery. Here we consider a more realistic version: exhibits now have size and may have different costs. Moreover the meaning of guarding is relaxed: we use a new concept, that of watching an expensive art item, i.e. overseeing a part of the item. The main result of the paper is that the problem of maximizing the total value of a guarded weighted boundary is APX-complete. This is shown by an appropriate gap-preserving reduction from the Max-5-occurrence-3-Sat problem. We also show that this technique can be applied to a number of maximization variations of the art gallery problem. In particular we consider the following problems: given a polygon with or without holes and k available guards, maximize a) the length of walls guarded and b) the total cost of paintings watched or overseen. We prove that all the above problems are APX-complete