Related papers: Barrier Coverage with Non-uniform Lengths to Minim…
In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…
This paper deals with the accomplishment of total area coverage of an arbitrary region using sensors with a finite sensing radius of rs. For a given region, we aim to obtain a deterministic placement of sensors which, apart from ensuring…
We show, assuming the (randomized) Gap Exponential Time Hypothesis (Gap-ETH), that the following tasks cannot be done in $T(k) \cdot N^{o(k)}$-time for any function $T$ where $N$ denote the input size: - $\left(1 - \frac{1}{e} +…
Given a set $P$ of $n$ points and a set $S$ of $m$ weighted disks in the plane, the disk coverage problem asks for a subset of disks of minimum total weight that cover all points of $P$. The problem is NP-hard. In this paper, we consider a…
We consider the problem of finding patrol schedules for $k$ robots to visit a given set of $n$ sites in a metric space. Each robot has the same maximum speed and the goal is to minimize the weighted maximum latency of any site, where the…
Given $n$ points in a circular region $C$ in the plane, we study the problems of moving the $n$ points to its boundary to form a regular $n$-gon such that the maximum (min-max) or the sum (min-sum) of the Euclidean distances traveled by the…
Given a set $P$ of $n$ points and a set $S$ of $n$ weighted disks in the plane, the disk coverage problem is to compute a subset of disks of smallest total weight such that the union of the disks in the subset covers all points of $P$. The…
We develop a randomized approximation algorithm for the classical maximum coverage problem, which given a list of sets $A_1,A_2,\cdots, A_m$ and integer parameter $k$, select $k$ sets $A_{i_1}, A_{i_2},\cdots, A_{i_k}$ for maximum union…
Covering a bounded region with minimum number of homogeneous sensor nodes is a NP-complete problem \cite{Li09}. In this paper we have proposed an {\it id} based distributed algorithm for optimal coverage in an unbounded region. The proposed…
We provide an O(log log OPT)-approximation algorithm for the problem of guarding a simple polygon with guards on the perimeter. We first design a polynomial-time algorithm for building epsilon-nets of size O(1/epsilon log log 1/epsilon) for…
The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed…
The minimum constraint removal problem seeks to find the minimum number of constraints, i.e., obstacles, that need to be removed to connect a start to a goal location with a collision-free path. This problem is NP-hard and has been studied…
In this paper, we first remodel the line coverage as a 1D discrete problem with co-linear targets. Then, an order-based greedy algorithm, called OGA, is proposed to solve the problem optimally. It will be shown that the existing order in…
We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at…
The art gallery problem enquires about the least number of guards that are sufficient to ensure that an art gallery, represented by a polygon $P$, is fully guarded. In 1998, the problems of finding the minimum number of point guards, vertex…
A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations,…
Let $\mathcal{W} \subset \mathbb{R}^2$ be a planar polygonal environment (i.e., a polygon potentially with holes) with a total of $n$ vertices, and let $A,B$ be two robots, each modeled as an axis-aligned unit square, that can translate…
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…
$\delta$-Covering, for some covering range $\delta>0$, is a continuous facility location problem on undirected graphs where all edges have unit length. The facilities may be positioned on the vertices as well as on the interior of the…
A fundamental problem in wireless sensor networks is to connect a given set of sensors while minimizing the \emph{receiver interference}. This is modeled as follows: each sensor node corresponds to a point in $\mathbb{R}^d$ and each…