More Like this

1. Optimal Sensor Placement for Kalman Filtering in Stochastically Forced Consensus Networks

   https://doi.org/10.1109/CDC.2018.8619288  

   Ye, Lintao ; Roy, Sandip ; Sundaram, Shreyas ( December 2018 , 2018 IEEE Conference on Decision and Control (CDC))

   Given a linear dynamical system affected by noise, we consider the problem of optimally placing sensors (at design-time) subject to certain budget constraints to minimize the trace of the steady-state error covariance of the Kalman filter. Previous work has shown that this problem is NP-hard in general. In this paper, we impose additional structure by considering systems whose dynamics are given by a stochastic matrix corresponding to an underlying consensus network. In the case when there is a single input at one of the nodes in a tree network, we provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. However, we show that when the network has multiple inputs, the optimal sensor placement problem becomes NP-hard.
2. Proportional Volume Sampling and Approximation Algorithms for A-Optimal Design

   https://doi.org/doi:10.1137/1.9781611975482.84  

   Nikolov, A ; Singh, M. ; Tantipongpipat, U. ( January 2019 , Symposium on Discrete Algorithms (SODA))

   We study the A-optimal design problem where we are given vectors υ1, …, υn ∊ ℝd, an integer k ≥ d, and the goal is to select a set S of k vectors that minimizes the trace of (∑i∊Svivi⊺)−1. Traditionally, the problem is an instance of optimal design of experiments in statistics [35] where each vector corresponds to a linear measurement of an unknown vector and the goal is to pick k of them that minimize the average variance of the error in the maximum likelihood estimate of the vector being measured. The problem also finds applications in sensor placement in wireless networks [22], sparse least squares regression [8], feature selection for k-means clustering [9], and matrix approximation [13, 14, 5]. In this paper, we introduce proportional volume sampling to obtain improved approximation algorithms for A-optimal design. Given a matrix, proportional volume sampling involves picking a set of columns S of size k with probability proportional to µ(S) times det(∑i∊Svivi⊺) for some measure µ. Our main result is to show the approximability of the A-optimal design problem can be reduced to approximate independence properties of the measure µ. We appeal to hardcore distributions as candidate distributions µ that allow usmore »to obtain improved approximation algorithms for the A-optimal design. Our results include a d-approximation when k = d, an (1 + ∊)-approximation when and -approximation when repetitions of vectors are allowed in the solution. We also consider generalization of the problem for k ≤ d and obtain a k-approximation. We also show that the proportional volume sampling algorithm gives approximation algorithms for other optimal design objectives (such as D-optimal design [36] and generalized ratio objective [27]) matching or improving previous best known results. Interestingly, we show that a similar guarantee cannot be obtained for the E-optimal design problem. We also show that the A-optimal design problem is NP-hard to approximate within a fixed constant when k = d.« less
3. Fine-Grained Trajectory Optimization of Multiple UAVs for Efficient Data Gathering from WSNs

   https://doi.org/10.1109/TNET.2020.3027555  

   Luo, Chuanwen ; Satpute, Meghana N. ; Li, Deying ; Wang, Yongcai ; Chen, Wenping ; Wu, Weili ( February 2021 , IEEE/ACM Transactions on Networking)

   The increasing availability of autonomous smallsize Unmanned Aerial Vehicles (UAVs) has provided a promising way for data gathering from Wireless Sensor Networks (WSNs) with the advantages of high mobility, flexibility, and good speed. However, few works considered the situations that multiple UAVs are collaboratively used and the fine-grained trajectory plans of multiple UAVs are devised for collecting data from network including detailed traveling and hovering plans of them in the continuous space. In this paper, we investigate the problem of the Fine-grained Trajectory Plan for multi-UAVs (FTP), in which m UAVs are used to collect data from a given WSN, where m ≥ 1. The problem entails not only to find the flight paths of multiple UAVs but also to design the detailed hovering and traveling plans on their paths for efficient data gathering from WSN. The objective of the problem is to minimize the maximum flight time of UAVs such that all sensory data of WSN is collected by the UAVs and transported to the base station. We first propose a mathematical model of the FTP problem and prove that the problem is NP-hard. To solve the FTP problem, we first study a special case of the FTP problemmore »when m = 1, called FTP with Single UAV (FTPS) problem. Then we propose a constantfactor approximation algorithm for the FTPS problem. Based on the FTPS problem, an approximation algorithm for the general version of the FTP problem when m > 1 is further proposed, which can guarantee a constant factor of the optimal solution. Afterwards, the proposed algorithms are verified by extensive simulations.« less
4. Time-Dependent Shortest Path Problems with Penalties and Limits on Waiting

   https://doi.org/10.1287/ijoc.2020.0985  

   He, Edward ; Boland, Natashia ; Nemhauser, George ; Savelsbergh, Martin ( January 2020 , INFORMS Journal on Computing)

   Waiting at the right location at the right time can be critically important in certain variants of time-dependent shortest path problems. We investigate the computational complexity of time-dependent shortest path problems in which there is either a penalty on waiting or a limit on the total time spent waiting at a given subset of the nodes. We show that some cases are nondeterministic polynomial-time hard, and others can be solved in polynomial time, depending on the choice of the subset of nodes, on whether waiting is penalized or constrained, and on the magnitude of the penalty/waiting limit parameter. Summary of Contributions: This paper addresses simple yet relevant extensions of a fundamental problem in Operations Research: the Shortest Path Problem (SPP). It considers time-dependent variants of SPP, which can account for changing traffic and/or weather conditions. The first variant that is tackled allows for waiting at certain nodes but at a cost. The second variant instead places a limit on the total waiting. Both variants have applications in transportation, e.g., when it is possible to wait at certain locations if the benefits outweigh the costs. The paper investigates these problems using complexity analysis and algorithm design, both tools from the fieldmore »of computing. Different cases are considered depending on which of the nodes contribute to the waiting cost or waiting limit (all nodes, all nodes except the origin, a subset of nodes…). The computational complexity of all cases is determined, providing complexity proofs for the variants that are NP-Hard and polynomial time algorithms for the variants that are in P.« less
5. Minimum Wireless Charger Placement with Individual Energy Requirement

   https://doi.org/10.1007/978-3-030-64843-5_47  

   Xingjian Ding, Jianxiong Guo ( December 2020 , Cocoa)

   Supply energy to battery-powered sensor devices by deploying wireless chargers is a promising way to prolong the operation time of wireless sensor networks, and has attracted much attention recently. Existing works focus on maximizing the total received charging power of the network. However, this may face the unbalanced energy allocation problem, which is not beneficial to prolong the operation time of wireless sensor networks. In this paper, we consider the individual energy requirement of each sensor node, and study the problem of minimum charger placement. That is, we focus on finding a strategy for placing wireless chargers from a given candidate location set, such that each sensor node’s energy requirement can be met, meanwhile the total number of used chargers can be minimized. We show that the problem to be solved is NP-hard, and present two approximation algorithms which are based on the greedy scheme and relax rounding scheme, respectively. We prove that both of the two algorithms have performance guarantees. Finally, we validate the performance of our algorithms by performing extensive numerical simulations. Simulation results show the effectiveness of our proposed algorithms