The fully indecomposable matrix and its associated bipartite graph - An investigation of combinatorial and structural properties
Combinatorial properties of classes of nonnegative matrices
Roberts, E. J.↗
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Results for “combinatorial”
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The 3-D world modeling with updating capability based on combinatorial geometry
A 3-D world modeling technique using range data is discribed. Range data quantify the distances from the sensor focal plane to the object surface, i.e., the 3-D coordinates of discrete points on the object surface are known. The approach proposed herein for 3-D world modeling is based on the Combinatorial Geometry (CG) method which is widely used in Monte Carlo particle transport calculations. First, each measured point on the object surface is surrounded by a small sphere with a radius determined by the range to that point. Then, the 3-D shapes of the visible surfaces are obtained by taking the (Boolean) union of all the spheres. The result is an unambiguous representation of the object's boundary surfaces. The pre-learned partial knowledge of the environment can be also represented using the CG Method with a relatively small amount of data. Using the CG type of representation, distances in desired directions to boundary surfaces of various objects are efficiently calculated. This feature is particularly useful for continuously verifying the world model against the data provided by a range finder, and for integrating range data from successive locations of the robot during motion. The efficiency of the proposed approach is illustrated by simulations of a spherical robot in a 3-D room in the presence of moving obstacles and inadequate prelearned partial knowledge of the environment.
Goldstein, M.↗
Computational efficiency of parallel combinatorial OR-tree searches
The performance of parallel combinatorial OR-tree searches is analytically evaluated. This performance depends on the complexity of the problem to be solved, the error allowance function, the dominance relation, and the search strategies. The exact performance may be difficult to predict due to the nondeterminism and anomalies of parallelism. The authors derive the performance bounds of parallel OR-tree searches with respect to the best-first, depth-first, and breadth-first strategies, and verify these bounds by simulation. They show that a near-linear speedup can be achieved with respect to a large number of processors for parallel OR-tree searches. Using the bounds developed, the authors derive sufficient conditions for assuring that parallelism will not degrade performance and necessary conditions for allowing parallelism to have a speedup greater than the ratio of the numbers of processors. These bounds and conditions provide the theoretical foundation for determining the number of processors required to assure a near-linear speedup.
Li, Guo-Jie↗
Combinatorial FSK modulation for power-efficient high-rate communications
Deep-space and satellite communications systems must be capable of conveying high-rate data accurately with low transmitter power, often through dispersive channels. A class of noncoherent Combinatorial Frequency Shift Keying (CFSK) modulation schemes is investigated which address these needs. The bit error rate performance of this class of modulation formats is analyzed and compared to the more traditional modulation types. Candidate modulator, demodulator, and digital signal processing (DSP) hardware structures are examined in detail. System-level issues are also discussed.
Wagner, Paul K.↗
Combinatorial FSK modulation for power-efficient high-rate communications
Deep-space and satellite communications systems must be capable of conveying high-rate data accurately with low transmitter power, often through dispersive channels. A class of noncoherent Combinatorial Frequency Shift Keying (CFSK) modulation schemes is investigated which address these needs. The bit error rate performance of this class of modulation formats is analyzed and compared to the more traditional modulation types. Candidate modulator, demodulator, and digital signal processing (DSP) hardware structures are examined in detail. System-level issues are also discussed.
Wagner, Paul K.↗
Combinatorial pulse position modulation for power-efficient free-space laser communications
A new modulation technique called combinatorial pulse position modulation (CPPM) is presented as a power-efficient alternative to quaternary pulse position modulation (QPPM) for direct-detection, free-space laser communications. The special case of 16C4PPM is compared to QPPM in terms of data throughput and bit error rate (BER) performance for similar laser power and pulse duty cycle requirements. The increased throughput from CPPM enables the use of forward error corrective (FEC) encoding for a net decrease in the amount of laser power required for a given data throughput compared to uncoded QPPM. A specific, practical case of coded CPPM is shown to reduce the amount of power required to transmit and receive a given data sequence by at least 4.7 dB. Hardware techniques for maximum likelihood detection and symbol timing recovery are presented.
Budinger, James M.↗
Thermal analysis of combinatorial solid geometry models using SINDA
Algorithms have been developed using Monte Carlo techniques to determine the thermal network parameters necessary to perform a finite difference analysis on Combinatorial Solid Geometry (CSG) models. Orbital and laser fluxes as well as internal heat generation are modeled to facilitate satellite modeling. The results of the thermal calculations are used to model the infrared (IR) images of targets and assess target vulnerability. Sample analyses and validation are presented which demonstrate code products.
Gerencser, Diane↗
Aerospace applications on integer and combinatorial optimization
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Padula, S. L.↗
Aerospace applications of integer and combinatorial optimization
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in solving combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on a large space structure and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Padula, S. L.↗
Aerospace Applications of Integer and Combinatorial Optimization
Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.
Padula, S. L.↗
Combinatorial Optimization of Heterogeneous Catalysts Used in the Growth of Carbon Nanotubes
Libraries of liquid-phase catalyst precursor solutions were printed onto iridium-coated silicon substrates and evaluated for their effectiveness in catalyzing the growth of multi-walled carbon nanotubes (MWNTs) by chemical vapor deposition (CVD). The catalyst precursor solutions were composed of inorganic salts and a removable tri-block copolymer (EO)20(PO)70(EO)20 (EO = ethylene oxide, PO = propylene oxide) structure-directing agent (SDA), dissolved in ethanol/methanol mixtures. Sample libraries were quickly assayed using scanning electron microscopy after CVD growth to identify active catalysts and CVD conditions. Composition libraries and focus libraries were then constructed around the active spots identified in the discovery libraries to understand how catalyst precursor composition affects the yield, density, and quality of the nanotubes. Successful implementation of combinatorial optimization methods in the development of highly active, carbon nanotube catalysts is demonstrated, as well as the identification of catalyst formulations that lead to varying densities and shapes of aligned nanotube towers.
Cassell, Alan M.↗
Solar Proton Transport within an ICRU Sphere Surrounded by a Complex Shield: Combinatorial Geometry
The 3DHZETRN code, with improved neutron and light ion (Z (is) less than 2) transport procedures, was recently developed and compared to Monte Carlo (MC) simulations using simplified spherical geometries. It was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in general combinatorial geometry. A more complex shielding structure with internal parts surrounding a tissue sphere is considered and compared against MC simulations. It is shown that even in the more complex geometry, 3DHZETRN agrees well with the MC codes and maintains a high degree of computational efficiency.
Wilson, John W.↗
Switched Systems and Motion Coordination: Combinatorial Challenges
Problems of routing commercial air traffic in a terminal airspace encounter different constraints: separation assurance, aircraft performance limitations, regulations. The general setting of these problems is that of a switched control system. Such a system combines the differentiable motion of the aircraft with the combinatorial choices of choosing precedence when traffic routes merge and choosing branches when the routes diverge. This presentation gives an overview of the problem, the ATM context, related literature, and directions for future research.
terminal airspace↗
Combinatorial Auction-Based Strategic Deconfliction of Federated UTM Airspace
Unmanned Aerial Vehicles (UAVs) have become commonly used to perform a wide range of commercial activities such as cinematography and medical supply delivery. Consequently, regulators have become interested in designing UAV Traffic Management systems (UTMs) to coordinate UAV traffic among a collection of UAV operators. One framework which has been recently proposed for a UTM system is a combinatorial auction. In this framework, airspace is modelled as a 4D grid of space-time cells. UAV operators bid on cells which collectively form paths for their UAVs. Ideally, an airspace auction should reveal information about the current price of flight paths to bidders, allowing bidders to identify and bid on a select number of paths instead of placing as many bids as possible in the hopes of stumbling on a cheap path. Revealing too much information, however, can allow bad actors to place bids which are intended not to win but to raise the price that a rival bidder must pay. We address these twin challenges with a new information revelation framework which provides bidders with wide-ranging pricing information while suppressing bad actors. We evaluate our framework on scenarios based on a Japan Aerospace Exploration Agency (JAXA) case study and find that it can scale to thousands of bids.
Christopher J C Leet↗
Communications systems research - Combinatorial communication
Cross correlation of reverse maximal length shift register sequences
Source record↗
A prototype combinatorial scheduler for space-borne observational instruments
A prototype scheduler has been developed for observations to be carried out by the NASA Gamma Ray Observatory. The purpose of the scheduling system is to provide an automated method to determine optimized schedules conforming to all scheduling guidelines. Strategies used in creating COMPTEL/EGRET schedules and in scheduling OSSE targets are examined. It is concluded that the hybrid scheduler creates optimal schedules, or very nearly optimal schedules, and reduces the estimated scheduling time by 18 or 19 orders of magnitude, from about 10 to the 14th years to as few as 561 seconds.
Gilstrap, Lewey O.↗
Learning dominance relations in combinatorial search problems
Dominance relations commonly are used to prune unnecessary nodes in search graphs, but they are problem-dependent and cannot be derived by a general procedure. The authors identify machine learning of dominance relations and the applicable learning mechanisms. A study of learning dominance relations using learning by experimentation is described. This system has been able to learn dominance relations for the 0/1-knapsack problem, an inventory problem, the reliability-by-replication problem, the two-machine flow shop problem, a number of single-machine scheduling problems, and a two-machine scheduling problem. It is considered that the same methodology can be extended to learn dominance relations in general.
Yu, Chee-Fen↗
Hopf-algebraic structure of combinatorial objects and differential operators
A Hopf-algebraic structure on a vector space which has as basis a family of trees is described. Some applications of this structure to combinatorics and to differential operators are surveyed. Some possible future directions for this work are indicated.
Grossman, Robert↗