Journal ArticleDOI
Cycle bases of minimal measure for the structural analysis of skeletal structures by the flexibility method
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A procedure to construct a finite sub-set of the cycle vector space containing the elements of all minimal bases makes the generation of the required basis feasible by a finite procedure, such as Welsh's generalization of the Kruskal algorithm.Abstract:
The development of the flexibility method of analysis of skeletal structures has been hindered by the difficulty of determining a suitable statical basis on which to form the flexibility matrix. A combinatorial approach reduces the difficulty to one of selecting a minimal basis of the cycle vector space. After an introduction to flexibility analysis and a brief review of earlier work using combinatorics, the paper presents a procedure to construct a finite sub-set of the cycle vector space containing the elements of all minimal bases. This makes the generation of the required basis feasible by a finite procedure, such as Welsh's generalization of the Kruskal algorithm. It is thus possible to have an automatic method for the analysis of skeletal structures which uses an optimal combinatorial approach.read more
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Journal ArticleDOI
The H2O Southern Galactic Plane Survey (HOPS) – I. Techniques and H2O maser data
Andrew Walsh,Shari Breen,Tui Britton,Kate J. Brooks,Michael G. Burton,Maria Cunningham,James Green,Lisa Harvey-Smith,Luke Hindson,Luke Hindson,Melvin Hoare,B. Indermuehle,Paul A. Jones,Paul A. Jones,N. Lo,N. Lo,Steven N. Longmore,Steven N. Longmore,Vicki Lowe,Vicki Lowe,Chris Phillips,Cormac Purcell,Mark Thompson,James Urquhart,Maxim Voronkov,Graeme L. White,Matthew Whiting +26 more
TL;DR: The first results of the H2O Southern Galactic Plane Survey (HOPS) using the Mopra Radio Telescope with a broadband backend and a beam size of about 2 arcmin were reported in this paper.
Book ChapterDOI
A Faster Algorithm for Minimum Cycle Basis of Graphs
TL;DR: A 1-e approximation algorithm to compute a cycle basis which is at most 1+e times the weight of a minimum cycle basis in a graph G with m edges and n vertices.
Journal ArticleDOI
Implementing minimum cycle basis algorithms
Kurt Mehlhorn,Dimitrios Michail +1 more
TL;DR: In this article, the problem of computing a minimum cycle basis of an undirected graph G = (V,E) with n vertices and m edges was considered and an efficient O(m3 p mn2 log n) algorithm was proposed.
Journal ArticleDOI
A combinatorial optimization problem; optimal generalized cycle bases
TL;DR: In this article, a combinatorial optimization method is presented for selecting optimal generalized cycle bases corresponding to sparse flexibility matrices and a different technique based on a quasiexpansion process is developed which uses an intersection theorem for selecting independent elements for the bases.
Journal ArticleDOI
Minimum cycle bases: Faster and simpler
Kurt Mehlhorn,Dimitrios Michail +1 more
TL;DR: A very simple method for extracting a minimum cycle basis from the candidate set with running time O(n), which improves the running time for sparse graphs and in the undirected case by using bit-packing the authors improve theRunning time also in the case of dense graphs.
References
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Journal ArticleDOI
Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird
Journal ArticleDOI
A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures
Journal ArticleDOI
Cycle bases for the flexibility analysis of structures
TL;DR: In this paper, two methods are presented for the automatic selection of a cycle basis leading to a sparse flexibility matrix for the analysis of rigid-jointed skeletal structures, and a cycle ordering algorithm is also given to reduce the band width of the corresponding flexibility matrix.
Journal ArticleDOI
Kruskal's theorem for matroids
TL;DR: Kruskal's theorem for obtaining a minimal (maximal) spanning tree of a graph is shown to be a special case of a more general theorem for matroid spaces in which each element of the matroid has an associated weight as mentioned in this paper.
Journal ArticleDOI
Topological Aspects of Structural Linear Analysis: Improving the Conditioning of the Equations of Compatibility of a Multi‐Member Skeletal Structure by Use of the Knowledge of Topology
TL;DR: In this paper, the selection of a system of cut releases which would render a continuous skeletal structure statically determinate is governed principally by the topological and geometric characteristics of the structure, and to a lesser extent by its material properties.
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