Related papers: Approximation Algorithms for Minimum Sum of Moving…
This paper considers a movement minimization problem for mobile sensors. Given a set of $n$ point targets, the $k$-Sink Minimum Movement Target Coverage Problem is to schedule mobile sensors, initially located at $k$ base stations, to cover…
Given a line barrier and a set of mobile sensors distributed in the plane, the Minimizing Maximum Sensor Movement problem (MMSM) for \textcolor{black}{line barrier coverage} is to compute relocation positions for the sensors in the plane…
In this paper, we present the first constant-approximation algorithm for {\em budgeted sweep coverage problem} (BSC). The BSC involves designing routes for a number of mobile sensors (a.k.a. robots) to periodically collect information as…
We investigate multiple fundamental variants of the classic coordinated motion planning (CMP) problem for unit square robots in the plane under the $L_1$ metric. In coordinated motion planning, we are given two arrangements of $k$ robots…
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…
We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (t_j) and radii (r_j) that cover a given set of demand points Y in the plane at the smallest possible…
We study the \textit{min-sum uniform coverage} problem for a swarm of $n$ mobile robots on a given finite line segment and on a circle having finite positive radius, where the circle is given as an input. The robots must coordinate their…
This paper considers three related mobile robot multi-target sensory coverage and inspection planning problems in 2-D environments. In the first problem, a mobile robot must find the shortest path to observe multiple targets with a limited…
Given a $d$-dimensional continuous (resp. discrete) probability distribution $\mu$ and a discrete distribution $\nu$, the semi-discrete (resp. discrete) Optimal Transport (OT) problem asks for computing a minimum-cost plan to transport mass…
This paper focuses on the optimal sensor placement problem for the identification of pipe failure locations in large-scale urban water systems. The problem involves selecting the minimum number of sensors such that every pipe failure can be…
In this paper we consider two metric covering/clustering problems - \textit{Minimum Cost Covering Problem} (MCC) and $k$-clustering. In the MCC problem, we are given two point sets $X$ (clients) and $Y$ (servers), and a metric on $X \cup…
Given two point sets $S$ and $T$, the minimum-cost many-to-many matching with demands (MMD) problem is the problem of finding a minimum-cost many-to-many matching between $S$ and $T$ such that each point of $S$ (respectively $T$) is matched…
Evolution of large scale networks demand for efficient way of communication in the networks. One way to propagate information in the network is to find vertex cover. In this paper we describe a variant of vertex cover problem naming it…
We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…
The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting…
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…
Assume n wireless mobile sensors are initially dispersed in an ad hoc manner in a rectangular region. They are required to move to final locations so that they can detect any intruder crossing the region in a direction parallel to the sides…
In the minimum cost submodular cover problem (MinSMC), we are given a monotone nondecreasing submodular function $f\colon 2^V \rightarrow \mathbb{Z}^+$, a linear cost function $c: V\rightarrow \mathbb R^{+}$, and an integer $k\leq f(V)$,…
We provide improved upper and lower bounds for the Min-Sum-Radii (MSR) and Min-Sum-Diameters (MSD) clustering problems with a bounded number of clusters $k$. In particular, we propose an exact MSD algorithm with running-time $n^{O(k)}$. We…
Minimum sum vertex cover of an $n$-vertex graph $G$ is a bijection $\phi : V(G) \to [n]$ that minimizes the cost $\sum_{\{u,v\} \in E(G)} \min \{\phi(u), \phi(v) \}$. Finding a minimum sum vertex cover of a graph (the MSVC problem) is…