Graph products for configuration processing of space structures

Kaveh, A.; Koohestani, K.

doi:10.1016/j.compstruc.2007.11.005

Cited by 41 publications

(26 citation statements)

References 11 publications

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“…The geometry representation used here is based on the morphological representation scheme that has been developed and progressively improved in a series of work [31][32][33][34][35]. By adopting a graph-theoretic approach which is naturally suited for topological representation [36,37], this morphological scheme intrinsically defines a fully-connected structural geometry, thereby avoiding the common problems of checkerboard patterns and corner-node hinge connections that can afflict other geometry representation methods like the basic bit-array representations [38][39][40]. These advantageous features are gained without sacrificing efficiency and versatility to define a wide range of topologies and shape, hence it has been successfully demonstrated in diverse applications [41,42].…”

Section: Enhanced Morphological Representation Of Geometrymentioning

confidence: 99%

Target matching problems and an adaptive constraint strategy for multiobjective design optimization using genetic algorithms

Wang

Tai

2010

Computers & Structures

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Section: Enhanced Morphological Representation Of Geometrymentioning

confidence: 99%

Target matching problems and an adaptive constraint strategy for multiobjective design optimization using genetic algorithms

Wang

Tai

2010

Computers & Structures

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“…Graphs and in particular graph products arise in a variety of different contexts, from computer science [1,30] to theoretical biology [18,43], computational engineering [31,32] or just as natural structures in discrete mathematics [8,37,17,22,19]. Standard references with respect to graph products are due to Imrich, Klavžar, Douglas and Hammack [24,25,10].…”

Section: Introductionmentioning

confidence: 99%

A local prime factor decomposition algorithm

Hellmuth

2011

Discrete Mathematics

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This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the well-known "classical" prime factorization algorithm is strictly limited. This new PFD algorithm is based on a local approach that covers a graph by small factorizable subgraphs and then utilizes this information to derive the global factors. Therefore, we can take advantage of this approach and derive in addition a method for the recognition of approximate graph products. the classical PFD approach to this problem is strictly limited, since almost all graphs are prime, although they can have a product-like structure. In fact, even a very small perturbation, such as the deletion or insertion of a single edge, can destroy the product structure completely, modifying a product graph to a prime graph [4,45].The recognition of approximate products has been investigated by several authors, see e.g. [5,13,14,28,45,26,42,44,15,20,16,23]. In [28] and [45] the authors showed that Cartesian and strong product graphs can be uniquely reconstructed from each of its one-vertex-deleted subgraphs. Moreover, in [29] it is shown that k-vertex-deleted Cartesian product graphs can be uniquely reconstructed if they have at least k + 1 factors and each factor has more than k vertices. A polynomial-time algorithm for the reconstruction of one-vertex-deleted Cartesian product graphs is given in [7]. In [26,42,44] algorithms for the recognition of so-called graph bundles are provided. Graph bundles generalize the notion of graph products and can also be considered as approximate products.Another systematic investigation into approximate product graphs showed that a further practically viable approach can be based on local factorization algorithms, that cover a graph by factorizable small patches and attempt to stepwisely extend regions with product structures. This idea has been fruitful in particular for the strong product of graphs, where one benefits from the fact that the local product structure of neighborhoods is a refinement of the global factors [13,14]. In [13] the class of thin-neighborhood intersection coverable (NICE) graphs was introduced, and a quasi-linear time local factorization algorithm w.r.t. the strong product was devised. In [14] this approach was extended to a larger class of thin graphs which are whose local factorization is not finer than the global one, so-called locally unrefined graphs.In this contribution the results of [13] and [14] will be extended and generalized. The main result will be a new quasi-linear time local prime factorization algorithm w.r.t. the strong product that works for all graph classes. Moreover, this algorithm can be adapted for the recognition of approximate products. This new PFD algorithm is imp...

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“…These subgraphs, used in the formation of the entire model, are called the generators of that model. There are other graph products with useful applications in configuration processing [4].…”

Section: Graph Products With Specified Domainsmentioning

confidence: 99%

“…Configuration processing using graph products is developed, with eight different products [4]. In these products the entire domain is considered and therefore only regular models can be generated.…”

Section: Introductionmentioning

confidence: 99%