Showing papers on "Star (graph theory) published in 1996"
Patent•
26 Sep 1996TL;DR: In this article, a method for determining the attitude of a spacecraft by observing stars within a starfield is presented, where a set of star match groups are generated by matching pairs of stars observed by the detector with pairs of guide stars from a stored database.
Abstract: A method for determining the attitude of a spacecraft (1) by observing stars (2) within a starfield (3). A detector (13), camera electronics (14), and computer (15) located on board the spacecraft (1) are used to generate a set of star match groups by matching pairs of stars observed by the detector (13) with pairs of guide stars from a stored database (18) of guide stars. Match groups having small numbers of stars are eliminated. Non-eliminated match groups are validated. Redundant match groups are eliminated. A match group having the largest number of stars is selected. Finally, the attitude of the spacecraft (1) is derived from positions of guide stars within the selected match group. The guide star database (18) can be broken into an acquisition guide star database (8) and a supplementary guide star database (9). The field of view (20) of detector (13) can be broken into a grid of pixels overlaid by a grid of superpixels (21). The guide star pairs are preferably presorted in order of increasing angular separation. An identification matrix (IDGRP) can be used to speed the star identification process.
87 citations
64 citations
TL;DR: A new decomposition technique for hierarchical Cayley graphs is presented, which yields a very easy implementation of the divide and conquer paradigm for some problems on very complex architectures as the star graph or the pancake.
Abstract: This paper presents a new decomposition technique for hierarchical Cayley graphs. This technique yields a very easy implementation of the divide and conquer paradigm for some problems on very complex architectures as the star graph or the pancake. As applications, we introduce algorithms for broadcasting and prefix-like operations that improve the best known bounds for these problems. We also give the first nontrivial optimal gossiping algorithms for these networks. In star-graphs and pancakes with N=n! processors, our algorithms take less than [log N]+1.5n steps.
60 citations
TL;DR: This work investigates star graphs under the conditions offorbidden faulty sets, where all the neighbors of any node cannot be faulty simultaneously, and shows that under these conditions star graphs can tolerate upto (2n? 5) faulty nodes and the fault diameter is increased only by 2 in the worst case in presence of maximum number of faults.
59 citations
TL;DR: In this article, a subalgebra of the formal star algebra (with coefficients contained in the uniformly dense subspace of representative functions with respect to the canonical action of the unitary group) is constructed.
Abstract: Based on a closed formula for a star product of Wick type on CPn, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star algebra (with coefficients contained in the uniformly dense subspace of representative functions with respect to the canonical action of the unitary group) that consists of converging power series in the formal parameter, thereby giving an elementary algebraic proof of a convergence result already obtained by Cahen, Gutt, and Rawnsley. In this subalgebra the formal parameter can be substituted by a real number α: the resulting associative algebras are infinite dimensional, except for the case α=1/K, K a positive integer, where they turn out to be isomorphic to the finite‐dimensional algebra of linear operators in the Kth energy eigen‐ space of an isotropic harmonic oscillator with n+1 degrees of freedom. Other examples like the 2n torus and the Poincare disk are discussed.
56 citations
Posted Content•
TL;DR: In this paper, the symmetry and order of differentiation properties of the Fedosov star product of Weyl type have been studied for K-ahler manifolds, where the corresponding sequence of bidifferential operators differentiates its first argument in holomorphic directions and its second argument in antiholomorphic directions.
Abstract: In this letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of Wick type on every K\"ahler manifold by a straight forward generalization of the corresponding star product in $\mathbb C^n$: the corresponding sequence of bidifferential operators differentiates its first argument in holomorphic directions and its second argument in antiholomorphic directions. By a Fedosov type procedure we give an existence proof of such star products for any K\"ahler manifold.
54 citations
TL;DR: An effective branch and cut procedure coupled with a suitable separation procedure that identifies violated facets for fractional solutions to the relaxed formulation of the Steiner tree problem is developed.
Abstract: This paper deals with a Steiner tree-star problem that is a special case of the degree constrained node-weighted Steiner tree problem. This problem arises in the context of designing telecommunications networks for digital data service, provided by regional telephone companies. In this paper, we develop an effective branch and cut procedure coupled with a suitable separation procedure that identifies violated facets for fractional solutions to the relaxed formulation. Computational results indicate that large problem instances with up to 200 nodes can be solved within acceptable time bounds.
50 citations
TL;DR: In this article, invariant integrals of functions and forms over q-deformed Euclidean space and spheres in N dimensions are defined and shown to be positive definite, compatible with the star structure and to satisfy a cyclic property involving the D matrix of SOq(N).
Abstract: Invariant integrals of functions and forms over q‐deformed Euclidean space and spheres in N dimensions are defined and shown to be positive definite, compatible with the star structure and to satisfy a cyclic property involving the D matrix of SOq(N). The definition is based on spherical and radial integration. Stokes theorem is proved with and without spherical boundary terms, as well as on the sphere.
48 citations
TL;DR: It is shown that, up to isomorphism among digits used in labeling the vertices, the generators of the star graph are unique and the minimum number of extra dimensions needed to acquire i wildcard dimensions is derived for the star and bubble sort networks.
Abstract: The paper proposes designs of interconnection networks (graphs) which can tolerate link failures. The networks under study belong to a subclass of Cayley graphs whose generators are subsets of all possible transpositions. We specifically focus on star and bubble sort networks. Our approach is to augment existing dimensions (or generators) with one or more dimensions. If the added dimension is capable of replacing any arbitrary failed dimension, it is called a wildcard dimension. It is shown that, up to isomorphism among digits used in labeling the vertices, the generators of the star graph are unique. The minimum number of extra dimensions needed to acquire i wildcard dimensions is derived for the star and bubble sort networks. Interestingly, the optimally augmented star network coincides with the Transposition network, T/sub n/. Transposition networks are studied rigorously. These networks are shown to be optimally fault tolerant. T/sub n/ is also shown to possess wide containers with short length. Fault diameter of T/sub n/ is shown to be n. While the T can efficiently embed star and bubble sort graphs, it can also lend itself to an efficient embedding of meshes and hypercubes.
44 citations
TL;DR: A lower bound is given for the degree of diagnosability of the sequential diagnosis strategy (seq — t) in n − star multi-computer system.
42 citations
01 Jan 1996
TL;DR: In this paper, the authors proposed an approach to augment existing dimensions (or generators) with one or more dimensions, called a wildcard dimension, which is capable of replacing any arbitrary failed dimension, and derived the minimum number of extra dimensions needed to acquire i wildcard dimensions for the star and bubble sort networks.
Abstract: The paper proposes designs of interconnection networks (graphs) which can tolerate link failures. The networks under study belong to a subclass of Cayley graphs whose generators are subsets of all possible transpositions. We specifically foeus on star and bubble sort networks. Our approach is to augment existing dimensions (or generators) with one or more dimensions. If the added dimension is capable of replacing any arbitrary failed dimension, it is called a wildcard dimension. It is shown that, up to isomorphism among digits used in labeling the vertices, the generators of the star graph are unique. The minimum number of extra dimensions needed to acquire i wildcard dimensions is derived for the star and bubble-sort networks. Interestingly, the optimally augmented star network coincides with the Transposition network, T. Transposition networks are studied rigorously. These networks are shown to be optimally fault-tolerant. T, is also shown to possess wide containers with short length. Fault- diameter of T is shown to be n. While the T can efficiently embed star and bubde-sort graphs, it can also lend'itself to an efficient embedding of meshes and hypercubes. Index Terms-Bubble-sort graph, Cayley graph, embedding, fault diameter, fault tolerance, generator, permutation, star graph, transposition.
03 Jun 1996
TL;DR: This paper proposes and analyzes a new interconnection network called bubblesort star graph, which is the merger of the bubblesort graph and the star graph and presents the deadlock-free wormhole routing algorithm for the proposed network.
Abstract: In this paper, we propose and analyze a new interconnection network called bubblesort star graph, which is the merger of the bubblesort graph and the star graph. We present the deadlock-free wormhole routing algorithm for the proposed network. We also develop the method to embed a mesh into a bubblesort star graph with dilation two and expansion one. Besides, we use the recursive scheme to embed the multiple disjoint copies of the hypercube into a bubblesort star graph with all faults recovery capacity as well as constant expansion and dilation one or two. This reflects the fact that the embeddability of the bubblesort star graph is much better than that of the star graph.
TL;DR: In this article, an algorithm capable of real-time autonomous star recognition from large star catalogues, with minimal storage requirements, is described, based on a locally optimised binary tree-search technique that systematically divides the search space until a small set of stars is left in the identification set.
TL;DR: An algorithm for the rapid identification of star patterns is presented, which produces a reliable, orientation independent star identification faster than conventional serial techniques and adaptable to many types of mission and application.
Abstract: An algorithm for the rapid identification of star patterns is presented. The paradigm utilizes a novel star selection technique and a new binary tree- search technique to identify star configurations from large catalogues in a minimal time with low data storage requirements. Performance claims are supported by test data and identification results from a ground-based experimental star camera, the system consistently demonstrating a capability to identify numbers of stars in a single star camera image. Features include a search time scaling to the logarithm of the number of stars in the identification set, a reduced dependence on star magnitude data, and a method of accounting for camera measurement inaccuracy. The method is suitable for in-space application and offers the possibility of complete sky identification coverage using high accuracy star cameras. The approach produces a reliable, orientation independent star identification faster than conventional serial techniques and adaptable to many types of mission and application.
Journal Article•
TL;DR: This paper shows how to construct in a complete star graph an asymptotically balanced spanning tree, and in an incomplete star graph a near-balanced spanning tree.
Abstract: Efficiently solving the personalized broadcast problem in an interconnection network typically relies on finding an appropriate spanning tree in the network. In this paper, we show how to construct in a complete star graph an asymptotically balanced spanning tree, and in an incomplete star graph a near-balanced spanning tree. In both cases, the tree is shown to have the minimum height. In the literature, this problem has only been considered for the complete star graph, and the constructed tree is about 4/3 times taller than the one proposed in this paper.
Journal Article•
TL;DR: This paper characterises some star sign pattern matrices and linear tree sign patternMatrices that allow a nilpotent matrix and some of these matrices are fitted for star sign patterns.
Abstract: We characterise some star sign pattern matrices and linear tree sign pattern matrices that allow a nilpotent matrix.
TL;DR: In this article, a necessary and sufficient condition for the complete graph Kn to be decomposed into stars Sm1, Sm2, Sm3, Sm4, Sm5, Sm6, Sm7, Sm8, Sm9, Sm10, Sm11, Sm12, Sm13, Sm14, Sm15, Sm16, Sm17, Sm18, Sm19, Sm20, Sm21
Abstract: In this paper we prove the following result. Let m1 ≥ m2 ≥ … ≥ m1 be nonnegative integers. A necessary and sufficient condition for the complete graph Kn to be decomposed into stars Sm1, Sm2, …, Sm1 is . © 1996 John Wiley & Sons, Inc.
TL;DR: This work presents two ranking schemes for the star interconnection network both of which allow constant time order preserving communication and enables one to efficiently implement order preserving ASCEND/DESCEND class of algorithms.
Abstract: A node ranking scheme provides the necessary structural view for developing algorithms on a network. We present two ranking schemes for the star interconnection network both of which allow constant time order preserving communication. The first scheme is based on a hierarchical view of the star network. It enables one to efficiently implement order preserving ASCEND/DESCEND class of algorithms. This class includes several important algorithms such as the Fast Fourier Transform (FFT) and matrix multiplication. The other ranking scheme gives a flexible pipelined view of the star interconnection network and provides a suitable framework for implementation of pipelined algorithms.
TL;DR: Criteria to check if there exists any equivalent transformation when a delta-network or a star- network is given, and a criterion about a special star-network which has an unreliable center node to explain how to use it are provided.
Abstract: It is an open problem whether there exists an equivalent transformation between star reliability networks and delta reliability networks. We provide: criteria to check if there exists any equivalent transformation when a delta-network or a star-network is given, and a criterion about a special star-network which has an unreliable center node and give an example to explain how to use it.
Journal Article•
Proceedings Article•
01 May 1996
TL;DR: An interactive platform is developed based on the algorithm with which the author is able to construct star solids that resemble human faces.
Abstract: We introduce a computationally efficient method for interactive construction of implicitly represented star solids. These solids smoothly approximate control shapes that are defined by exact union and intersections over half-spaces containing the origin. Based on our algorithm, computation of a new solid shape when a new half-space is added or when the position of an existing half-space is changed can be performed in constant time and in space linear in the number of half-spaces. Our implicit shape construction is based on a family of non-polynomials called ray-linears [Akl93]. Computation of an implicitly represented shape is a root finding process and in general can be extremely difficult. However since ray-linear implicit representations can easily be parameterized, the computation of any ray-linearly represented shape simplifies to evaluation of a parametric equation instead of root finding. But the related parametric equations are non-polynomials and their complexity increases as the number of building blocks (in this case halfspaces) increases. Our algorithm makes the computation of this parametric equation independent of the number of half-spaces. We develop an interactive platform based on our algorithm with which we are able to construct star solids that resemble human faces. CR
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TL;DR: In this article, the stability of the star is not in danger, contrary to recent assertions, since massless neutrinos are exchanged in a neutron star, leading to long range interactions.
TL;DR: To determine the sky seen by the CT-601 star trackers, extensive star catalog generation capability has been developed for EOS-AMI attitude determination studies and properties of the resulting star field are assessed, including statistics of position errors, brightness (detector magnitude), variability, and spectral class.
Abstract: Star catalogs are essential for determining the expected performance of stellar-inertial attitude determination systems, such as that planned for the Earth Observation System AMI (EOS-AMI) mission. That spacecraft will use the CT-601 star trackers to maintain long-term attitude knowledge and gyros to measure short-term motion. To determine the sky seen by the CT-601 star trackers, extensive star catalog generation capability has been developed for EOS-AMI attitude determination studies. The present study begins with the Goddard Space Flight Center SKYMAP catalog as the source and continues with tracker star separation and spectral response properties. It rejects stars that are not usable because of excessive variability in intensity or excessive position error or for which accurate spectra are not available. This study also assesses properties of the resulting star field, including statistics of position errors, brightness (detector magnitude), variability, and spectral class. The resulting catalog is combined with models of the lunar and solar motion and EOS-AMI star tracker and orbital geometries to determine gaps in the star field induced by lunar blockage of the star trackers. The history of total star gaps over one year of EOS-AMI operations is assessed, with periods of both minimum and maximum gaps defined, as well as gap statistics. The geometry of the worst-case gap is illustrated. Additionally, the potential for planetary corruption of star measurements is assessed.
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TL;DR: In this article, the stability of the star is not in danger, contrary to recent assertions, since massless neutrinos are exchanged in a neutron star, leading to long range interactions.
Abstract: Massless neutrinos are exchanged in a neutron star, leading to long range interactions. Many body forces of this type follow and we resum them. Their net contribution to the total energy is negligible as compared to the star mass. The stability of the star is not in danger, contrary to recent assertions.