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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantum Networks: A New Platform for Aerospace

The ability to distribute entanglement between quantum nodes may unlock new capabilities in the future that include teleporting information across multinode networks, higher resolution detection via entangled sensor arrays, and measurements beyond the quantum limit enabled by networked atomic clocks. These new quantum networks also hold promise for the Aerospace community in areas such as deep space exploration, improved satellite communication, and synchronizing drone swarms. Although exciting, these applications are a long way off from providing a “real-world” benefit, as they have only been theoretically explored or demonstrated in small-scale experiments. An outstanding challenge is to identify near-term use cases for quantum networks; this may be an intriguing new area of interest for the aerospace community, as the quantum networking field would benefit from more multidisciplinary collaborations. This paper introduces quantum networking, discusses the difficulties in distributing entanglement within these networks, highlights recent progress toward this endeavor, and features two current case studies on mobile quantum nodes and an entangled clock network, both of which are relevant to the aerospace community.

Engineering↗
NASA NTRS2015

Core Analysis Combining MT (TIPPER) and Dielectric Sensors (Sans EC) in Earth and Space

On terrestrial planets and moons of our solar system cores reveal details about a geological structure's formation, content, and history. The strategy for the search for life is focused first on finding water which serves as a universal solvent, and identifying the rocks which such solvent act upon to release the constituent salts, minerals, ferrites, and organic compounds and chemicals necessary for life. Dielectric spectroscopy measures the dielectric properties of a medium as a function of frequency. Reflection measurements in the frequency range from 300 kHz to 300 MHz were carried out using RF and microwave network analyzers interrogating SansEC Sensors placed on clean geological core samples. These were conducted to prove the concept feasibility of a new geology instrument useful in the field and laboratory. The results show that unique complex frequency spectra can be acquired for a variety of rock core samples. Using a combination of dielectric spectroscopy and computer simulation techniques the magnitude and phase information of the frequency spectra can be converted to dielectric spectra. These low-frequency dielectric properties of natural rock are unique, easily determined, and useful in characterizing geology. TIPPER is an Electro-Magnetic Passive-Source Geophysical Method for Detecting and Mapping Geothermal Reservoirs and Mineral Resources. This geophysical method uses distant lightning and solar wind activity as its energy source. The most interesting deflections are caused by the funneling of electrons into more electrically conductive areas like mineralized faults, water or geothermal reservoirs. We propose TIPPER to be used with SansEC for determining terrain/ocean chemistry, ocean depth, geomorphology of fracture structures, and other subsurface topography characteristics below the ice crust of Jovian moons. NASA envisions lander concepts for exploration of these extraterrestrial icy surfaces and the oceans beneath. One such concept would use a nuclear powered heated tip for melting through the ice sheath of Europa and inserting a down hole SansEC with TIPPER interface. NASA's Juno space probe already on the way to Jupiter as part of the Exploration New Frontiers Program and the planned Europa mission will conduct detailed reconnaissance of Jupiter's moon Europa and investigate whether the icy moon could harbor conditions suitable for life. It has already been observed that Jovian moons have auroras that may serve as naturally occurring active energy sources for a TIPPER instrument.

Mound, Michael C.↗
NASA NTRS2013

NASA Tech Briefs, January 2013

Topics include: Single-Photon-Sensitive HgCdTe Avalanche Photodiode Detector; Surface-Enhanced Raman Scattering Using Silica Whispering-Gallery Mode Resonators; 3D Hail Size Distribution Interpolation/Extrapolation Algorithm; Color-Changing Sensors for Detecting the Presence of Hypergolic Fuels; Artificial Intelligence Software for Assessing Postural Stability; Transformers: Shape-Changing Space Systems Built with Robotic Textiles; Fibrillar Adhesive for Climbing Robots; Using Pre-Melted Phase Change Material to Keep Payloads in Space Warm for Hours without Power; Development of a Centrifugal Technique for the Microbial Bioburden Analysis of Freon (CFC-11); Microwave Sinterator Freeform Additive Construction System (MS-FACS); DSP/FPGA Design for a High-Speed Programmable S-Band Space Transceiver; On-Chip Power-Combining for High-Power Schottky Diode-Based Frequency Multipliers; FPGA Vision Data Architecture; Memory Circuit Fault Simulator; Ultra-Compact Transputer-Based Controller for High-Level, Multi-Axis Coordination; Regolith Advanced Surface Systems Operations Robot Excavator; Magnetically Actuated Seal; Hybrid Electrostatic/Flextensional Mirror for Lightweight, Large-Aperture, and Cryogenic Space Telescopes; System for Contributing and Discovering Derived Mission and Science Data; Remote Viewer for Maritime Robotics Software; Stackfile Database; Reachability Maps for In Situ Operations; JPL Space Telecommunications Radio System Operating Environment; RFI-SIM: RFI Simulation Package; ION Configuration Editor; Dtest Testing Software; IMPaCT - Integration of Missions, Programs, and Core Technologies; Integrated Systems Health Management (ISHM) Toolkit; Wind-Driven Wireless Networked System of Mobile Sensors for Mars Exploration; In Situ Solid Particle Generator; Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature; Rad-Tolerant, Thermally Stable, High-Speed Fiber-Optic Network for Harsh Environments; Towed Subsurface Optical Communications Buoy; High-Collection-Efficiency Fluorescence Detection Cell; Ultra-Compact, Superconducting Spectrometer-on-a-Chip at Submillimeter Wavelengths; UV Resonant Raman Spectrometer with Multi-Line Laser Excitation; Medicine Delivery Device with Integrated Sterilization and Detection; Ionospheric Simulation System for Satellite Observations and Global Assimilative Model Experiments - ISOGAME; Airborne Tomographic Swath Ice Sounding Processing System; flexplan: Mission Planning System for the Lunar Reconnaissance Orbiter; Estimating Torque Imparted on Spacecraft Using Telemetry; PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils; Multiple-Frame Detection of Subpixel Targets in Thermal Image Sequences; Metric Learning to Enhance Hyperspectral Image Segmentation; Basic Operational Robotics Instructional System; Sheet Membrane Spacesuit Water Membrane Evaporator; Advanced Materials and Manufacturing for Low-Cost, High-Performance Liquid Rocket Combustion Chambers; Motor Qualification for Long-Duration Mars Missions.

Source record↗
DOE OSTI2018

Toward a smart data transfer node

Scientific computing systems are becoming significantly more complex, with distributed teams and complex workflows spanning resources from telescopes and light sources to fast networks and Internet of Things sensor systems. In such settings, no single, centralized administrative team and software stack can coordinate and manage all resources used by a single application. Indeed, we have reached a critical limit in manageability using current human-in-the-loop techniques. We therefore argue that resources must begin to respond automatically, adapting and tuning their behavior in response to observed properties of scientific workflows. Over time, machine learning methods can be used to identify effective strategies for autonomic, goal-driven management behaviors that can be applied end-to-end across the scientific computing landscape. Using the data transfer nodes that are widely deployed in modern research networks as an example, we explore the architecture, methods, and algorithms needed for a smart data transfer node to support future scientific computing systems that self-tune and self-manage.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Lunar Relay Satellite Network for Space Exploration: Architecture, Technologies and Challenges

NASA is planning a series of short and long duration human and robotic missions to explore the Moon and then Mars. A key objective of these missions is to grow, through a series of launches, a system of systems infrastructure with the capability for safe and sustainable autonomous operations at minimum cost while maximizing the exploration capabilities and science return. An incremental implementation process will enable a buildup of the communication, navigation, networking, computing, and informatics architectures to support human exploration missions in the vicinities and on the surfaces of the Moon and Mars. These architectures will support all space and surface nodes, including other orbiters, lander vehicles, humans in spacesuits, robots, rovers, human habitats, and pressurized vehicles. This paper describes the integration of an innovative MAC and networking technology with an equally innovative position-dependent, data routing, network technology. The MAC technology provides the relay spacecraft with the capability to autonomously discover neighbor spacecraft and surface nodes, establish variable-rate links and communicate simultaneously with multiple in-space and surface clients at varying and rapidly changing distances while making optimum use of the available power. The networking technology uses attitude sensors, a time synchronization protocol and occasional orbit-corrections to maintain awareness of its instantaneous position and attitude in space as well as the orbital or surface location of its communication clients. A position-dependent data routing capability is used in the communication relay satellites to handle the movement of data among any of multiple clients (including Earth) that may be simultaneously in view; and if not in view, the relay will temporarily store the data from a client source and download it when the destination client comes into view. The integration of the MAC and data routing networking technologies would enable a relay satellite system to provide end-to-end communication services for robotic and human missions in the vicinity, or on the surface of the Moon with a minimum of Earth-based operational support.

Bhasin, Kul B.↗
NASA NTRS2003

Extraction of Qualitative Features from Sensor Data Using Windowed Fourier Transform

In this paper, we use Matlab to model the health monitoring of a system through the information gathered from sensors. This implies assessment of the condition of the system components. Once a normal mode of operation is established any deviation from the normal behavior indicates a change. This change may be due to a malfunction of an element, a qualitative change, or a change due to a problem with another element in the network. For example, if one sensor indicates that the temperature in the tank has experienced a step change then a pressure sensor associated with the process in the tank should also experience a step change. The step up and step down as well as sensor disturbances are assumed to be exponential. An RC network is used to model the main process, which is step-up (charging), drift, and step-down (discharging). The sensor disturbances and spike are added while the system is in drift. The system is allowed to run for a period equal to three time constant of the main process before changes occur. Then each point of the signal is selected with a trailing data collected previously. Two trailing lengths of data are selected, one equal to two time constants of the main process and the other equal to two time constants of the sensor disturbance. Next, the DC is removed from each set of data and then the data are passed through a window followed by calculation of spectra for each set. In order to extract features the signal power, peak, and spectrum are plotted vs time. The results indicate distinct shapes corresponding to each process. The study is also carried out for a number of Gaussian distributed noisy cases.

Amini, Abolfazl M.↗
DOE OSTI2021

Novel Data Driven Noise Emulation Framework using Deep Neural Network for Generating Synthetic PMU Measurements

Sensors play a critical role in supporting day-to-day grid operations and they are essential to operator’s decision-making process. Furthermore, sensors and sensor behaviors need to be emulated with grid simulations to perform modeling studies and to design cutting edge power systems applications. Ensuring the accurate behavior of these applications requires accurate emulation of sensors and pertinent signals. However, most grid simulators and modeling tools assume either zero error scenarios or simplistic noise models that may not always correlate to real-world sensors. To address the above issue, this work presents an initial study on the noise characteristics of phasor measurement units (PMUs), along with models for recreating their unique noise signatures. The proposed methods (both analytical and machine-learning-based) provide a substantial increase in a sensor’s model fidelity, a feature that can be leveraged by an end-user application to yield more accurate system representations. The proposed methods were then applied to micro PMU data from the EPFL microgrid campus to extract sensor noise profiles. This data was used to train a deep learning model, which was tested to emulate the noise characteristics present in actual signals. Based on the observed results and the employed data-driven methodology, the proposed methods may be adapted to replicate the behavior of other grid sensors and power new applications capable of detecting sensor degradation and eventual device failures in near real-time.

PMU, noise emulation, synthetic measurements, deep↗
NASA NTRS1998

Lightning Radio Source Retrieval Using Advanced Lightning Direction Finder (ALDF) Networks

A linear algebraic solution is provided for the problem of retrieving the location and time of occurrence of lightning ground strikes from an Advanced Lightning Direction Finder (ALDF) network. The ALDF network measures field strength, magnetic bearing and arrival time of lightning radio emissions. Solutions for the plane (i.e., no Earth curvature) are provided that implement all of tile measurements mentioned above. Tests of the retrieval method are provided using computer-simulated data sets. We also introduce a quadratic planar solution that is useful when only three arrival time measurements are available. The algebra of the quadratic root results are examined in detail to clarify what portions of the analysis region lead to fundamental ambiguities in source location. Complex root results are shown to be associated with the presence of measurement errors when the lightning source lies near an outer sensor baseline of the ALDF network. In the absence of measurement errors, quadratic root degeneracy (no source location ambiguity) is shown to exist exactly on the outer sensor baselines for arbitrary non-collinear network geometries. The accuracy of the quadratic planar method is tested with computer generated data sets. The results are generally better than those obtained from the three station linear planar method when bearing errors are about 2 deg. We also note some of the advantages and disadvantages of these methods over the nonlinear method of chi(sup 2) minimization employed by the National Lightning Detection Network (NLDN) and discussed in Cummins et al.(1993, 1995, 1998).

Koshak, William J.↗
NASA NTRS2005

Strawman Philosophical Guide for Developing International Network of GPM GV Sites

The creation of an international network of ground validation (GV) sites that will support the Global Precipitation Measurement (GPM) Mission's international science programme will require detailed planning of mechanisms for exchanging technical information, GV data products, and scientific results. An important component of the planning will be the philosophical guide under which the network will grow and emerge as a successful element of the GPM Mission. This philosophical guide should be able to serve the mission in developing scientific pathways for ground validation research which will ensure the highest possible quality measurement record of global precipitation products. The philosophical issues, in this regard, partly stem from the financial architecture under which the GV network will be developed, i.e., each participating country will provide its own financial support through committed institutions -- regardless of whether a national or international space agency is involved.At the 1st International GPM Ground Validation Workshop held in Abingdon, UK in November-2003, most of the basic tenants behind the development of the international GV network were identified and discussed. Therefore, with this progress in mind, this presentation is intended to put forth a strawman philosophical guide supporting the development of the international network of GPM GV sites, noting that the initial progress has been reported in the Proceedings of the 1st International GPM GV Workshop -- available online. The central philosophical issues themselves, all flow from the fact that each participating institution can only bring to the table, GV facilities and scientific personnel that are affordable to the sanctioning (funding) national agency (be that a research, research-support, or operational agency). This situation imposes on the network, heterogeneity in the measuring sensors, data collection periods, data collection procedures, data latencies, and data reporting capabilities. Therefore, in order for the network to be effective in supporting the central scientific goals of the GPM mission, there must be a basic agreed upon doctrine under which the network participants function vis-a-vis: (1) an overriding set of general scientific requirements, (2) a minimal set of policies governing the free flow of GV data between the scientific participants, (3) a few basic definitions concerning the prioritization of measurements and their respective value to the mission, (4) a few basic procedures concerning data formats, data reporting procedures, data access, and data archiving, and (5) a simple means to differentiate GV sites according to their level of effort and ability to perform near real-time data acquisition - data reporting tasks. Most important, in case they choose to operate as a near real-time data collection-data distribution site, they would be expected to operate under a fairly narrowly defined protocol needed to ensure smooth GV support operations. This presentation will suggest measures responsive to items (1) - (5) from which to proceed,. In addition, this presentation will seek to stimulate discussion and debate concerning how much heterogeneity is tolerable within the eventual GV site network, given that the any individual GV site can only be considered scientifically useful if it supports the achievement of the central GPM Mission goals. Only ground validation research that has a direct connection to the space mission should be considered justifiable given the overarching scientific goals of the mission. Therefore each site will have to seek some level of accommodation to what the GPM Mission requires in the way of retrieval error characterization, retrieval error detection and reporting, and generation of GV data products that support assessment and improvement of the mission's standard precipitation retrieval algorithms. These are all important scientific issues that will be best resolved in open scientific debate.

Smith, Eric A.↗
DOE OSTI2022

Prospects of federated machine learning in fluid dynamics

Physics-based models have been mainstream in fluid dynamics for developing predictive models. In recent years, machine learning has offered a renaissance to the fluid community due to the rapid developments in data science, processing units, neural network based technologies, and sensor adaptations. So far in many applications in fluid dynamics, machine learning approaches have been mostly focused on a standard process that requires centralizing the training data on a designated machine or in a data center. In this article, we present a federated machine learning approach that enables localized clients to collaboratively learn an aggregated and shared predictive model while keeping all the training data on each edge device. We demonstrate the feasibility and prospects of such a decentralized learning approach with an effort to forge a deep learning surrogate model for reconstructing spatiotemporal fields. Our results indicate that federated machine learning might be a viable tool for designing highly accurate predictive decentralized digital twins relevant to fluid dynamics.

36 MATERIALS SCIENCE↗
NASA NTRS2014

An Intrinsic Fiber-Optic Sensor for Structure Lightning Current Measurement

An intrinsic optical-fiber sensor based on Faraday Effect is developed that is highly suitable for measuring lightning current on aircraft, towers and complex structures. Originally developed specifically for aircraft installations, it is light-weight, non-conducting, structure conforming, and is immune to electromagnetic interference, hysteresis and saturation. It can measure total current down to DC. When used on lightning towers, the sensor can help validate other sensors and lightning detection network measurements. Faraday Effect causes light polarization to rotate when the fiber is exposed to a magnetic field in the direction of light propagation. Thus, the magnetic field strength can be determined from the light polarization change. By forming closed fiber loops and applying Ampere's law, measuring the total light rotation yields the total current enclosed. A broadband, dual-detector, reflective polarimetric scheme allows measurement of both DC component and AC waveforms with a 60 dB dynamic range. Two systems were built that are similar in design but with slightly different sensitivities. The 1310nm laser system can measure 300 A - 300 kA, and has a 15m long sensing fiber. It was used in laboratory testing, including measuring current on an aluminum structure simulating an aircraft fuselage or a lightning tower. High current capabilities were demonstrated up to 200 kA at a lightning test facility. The 1550nm laser system can measure 400 A - 400 kA and has a 25m fiber length. Used in field measurements, excellent results were achieved in the summer of 2012 measuring rocket-triggered lightning at the International Center for Lightning Research and Testing (ICLRT), Camp Blanding, Florida. In both systems increased sensitivity can be achieved with multiple fiber loops. The fiber optic sensor provides many unique capabilities not currently possible with traditional sensors. It represents an important new tool for lightning current measurement where low weight, complex shapes, large structure dimension, large current, and low frequency capabilities are important considerations.

Nguyen, Truong X.↗
DOE OSTI2018

Digital acoustic sensor performance across the infrasound range in non-isolated conditions

The next generation of acoustic sensors is emerging to supplement legacy sensors traditionally used in regional and global networks. These devices operate under similar principles as traditional sensors, without the need of a separate external digitizer. The calibration of these sensors against their predecessors is crucial to the modernization of conventional technologies. This work describes the characterization of the next-generation MB3 digital microbarometer and the iPrecision smartphone microphone in a non-isolated calibration room across the infrasound (i.e., 0.01–20 Hz) range. The intent is to evaluate nominal instrument performance before deployment. A portable rotary subwoofer is used as a controllable infrasound source to generate single-tone sinusoidal and broadband noise pressure waves in a room configured for calibration purposes. For each device, comparison measurements are made, from which the digital sensitivity and the parametric response is developed. The results provide insight into the performance of the sensors in non-isolated environments. By overlapping the responses of the test sensors, digital sensor performance across the infrasound range can be benchmarked. These responses may serve as a double-reference scheme in future pressure measurements and digital calibrations of acoustic sensors.

47 OTHER INSTRUMENTATION↗
NASA NTRS1998

Emulating the visual receptive-field properties of MST neurons with a template model of heading estimation

We have proposed previously a computational neural-network model by which the complex patterns of retinal image motion generated during locomotion (optic flow) can be processed by specialized detectors acting as templates for specific instances of self-motion. The detectors in this template model respond to global optic flow by sampling image motion over a large portion of the visual field through networks of local motion sensors with properties similar to those of neurons found in the middle temporal (MT) area of primate extrastriate visual cortex. These detectors, arranged within cortical-like maps, were designed to extract self-translation (heading) and self-rotation, as well as the scene layout (relative distances) ahead of a moving observer. We then postulated that heading from optic flow is directly encoded by individual neurons acting as heading detectors within the medial superior temporal (MST) area. Others have questioned whether individual MST neurons can perform this function because some of their receptive-field properties seem inconsistent with this role. To resolve this issue, we systematically compared MST responses with those of detectors from two different configurations of the model under matched stimulus conditions. We found that the characteristic physiological properties of MST neurons can be explained by the template model. We conclude that MST neurons are well suited to support self-motion estimation via a direct encoding of heading and that the template model provides an explicit set of testable hypotheses that can guide future exploration of MST and adjacent areas within the superior temporal sulcus.

NASA Discipline Neuroscience↗
DOE OSTI2022

Application of Frequency Division Multiplexing and Neural Networks in the Operation and Diagnosis of the Stator Current and Shaft Position Sensors Used in Electric/Hybrid Vehicles

Fast, precise and robust sensing of currents and motor shaft angle is essential for the excellent performance of electric and hybrid vehicles (EV/HEV). Multiplexing techniques are commonly applied in data acquisition systems (DAQs) to digitize the signals sensed in EV/HEV drives. Frequency-division multiplexing (FDM) applied to get the signals from current sensors and resolver angular position sensor has advantages over conventional multiplexing approaches. However, problems such as aging and mechanical imperfections distort the outputs of those sensors, producing measurement errors of the angular position and currents. Conventional techniques designed to compensate for those errors cannot be applied in signals multiplexed in frequency. This paper proposes online techniques to detect and compensate for the distortions in the resolver sensor and current sensors. The demultiplexing process was adjusted to allow distortion detection and compensation. An auto-associative neural network (ANN) compensates for the current measurement error, while an energy-based technique is applied to compensate for the distortions in the resolver outputs. The obtained results show that the distortions were compensated, allowing a more accurate estimation of stator currents and angular position when FDM is applied in EV/HEV DAQs.

Pereira Pinto, Joao↗
DOE OSTI2016

Comparative Kinetic Analysis of Closed-Ended and Open-Ended Porous Sensors

Efficient mass transport through porous networks is essential for achieving rapid response times in sensing applications utilizing porous materials. In this work, we show that open-ended porous membranes can overcome diffusion challenges experienced by closed-ended porous materials in a microfluidic environment. A theoretical model including both transport and reaction kinetics is employed to study the influence of flow velocity, bulk analyte concentration, analyte diffusivity, and adsorption rate on the performance of open-ended and closed-ended porous sensors integrated with flow cells. The analysis shows that open-ended pores enable analyte flow through the pores and greatly reduce the response time and analyte consumption for detecting large molecules with slow diffusivities compared with closed-ended pores for which analytes largely flow over the pores. Experimental confirmation of the results was carried out with open- and closed-ended porous silicon (PSi) microcavities fabricated in flow-through and flow-over sensor configurations, respectively. The adsorption behavior of small analytes onto the inner surfaces of closed-ended and open-ended PSi membrane microcavities was similar. However, for large analytes, PSi membranes in a flow-through scheme showed significant improvement in response times due to more efficient convective transport of analytes. The experimental results and theoretical analysis provide quantitative estimates of the benefits offered by open-ended porous membranes for different analyte systems.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

AI-based Detection and Defense Against Cyberattacks in Distributed Energy Resources

This study will provide comprehensive artificial intelligence (AI)-based solution tools for network security, malware prevention, and sensor data anomaly detection for distributed energy resource (DER) research, development, and demonstration. DER technologies are energy systems (e.g., solar panels, wind turbines, and energy storage systems) that are often connected to the internet and thus vulnerable to cyberattacks. Cybersecurity should be of primary concern for DERs, which is why we propose an integrated multi-layer cyber-defense system for DERs. This system encompasses risk assessments, network security, malware prevention, and detection of anomalies in the sensor data. Implementation of a comprehensive risk assessment with an overview of the model architecture should be the primary step, and should include the potential impact of experiencing, at a given time, one or more cyberattacks on the system. The second step is to ensure that the network security includes firewalls, intrusion detection, and malware prevention. The third step is to provide solution tools that enable sensor data anomaly detection for DERs. By incorporating these considerations into DER research, development, and demonstration, organizations can help ensure the safety and security of their systems and protect against potential cyberattacks.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2017

Geometric Hitting Set for Segments of Few Orientations

In this paper, we study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks) using the fewest sensors (the “hitting points”). We give approximation algorithms for cases including (i) lines of 3 slopes in the plane, (ii) vertical lines and horizontal segments, (iii) pairs of horizontal/vertical segments. We give hardness and hardness of approximation results for these problems. Finally, we prove that the hitting set problem for vertical lines and horizontal rays is polynomially solvable.

97 MATHEMATICS AND COMPUTING↗