Embedded connectivity of some BC networks
Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topo...
Ausführliche Beschreibung
Autor*in: |
Zhao, Ying-Ze [verfasserIn] |
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Artikel |
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Sprache: |
Englisch |
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2022 |
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Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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Übergeordnetes Werk: |
Enthalten in: The journal of supercomputing - Springer US, 1987, 78(2022), 14 vom: 09. Mai, Seite 16605-16618 |
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Übergeordnetes Werk: |
volume:78 ; year:2022 ; number:14 ; day:09 ; month:05 ; pages:16605-16618 |
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DOI / URN: |
10.1007/s11227-022-04522-3 |
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OLC2079484338 |
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520 | |a Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. | ||
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10.1007/s11227-022-04522-3 doi (DE-627)OLC2079484338 (DE-He213)s11227-022-04522-3-p DE-627 ger DE-627 rakwb eng 004 620 VZ Zhao, Ying-Ze verfasserin aut Embedded connectivity of some BC networks 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. Embedded connectivity Fault-tolerance BC network Crossed cube Möbius cube Generalized product Li, Xiang-Jun (orcid)0000-0003-1194-1124 aut Ma, Meijie aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 14 vom: 09. Mai, Seite 16605-16618 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:14 day:09 month:05 pages:16605-16618 https://doi.org/10.1007/s11227-022-04522-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 14 09 05 16605-16618 |
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10.1007/s11227-022-04522-3 doi (DE-627)OLC2079484338 (DE-He213)s11227-022-04522-3-p DE-627 ger DE-627 rakwb eng 004 620 VZ Zhao, Ying-Ze verfasserin aut Embedded connectivity of some BC networks 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. Embedded connectivity Fault-tolerance BC network Crossed cube Möbius cube Generalized product Li, Xiang-Jun (orcid)0000-0003-1194-1124 aut Ma, Meijie aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 14 vom: 09. Mai, Seite 16605-16618 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:14 day:09 month:05 pages:16605-16618 https://doi.org/10.1007/s11227-022-04522-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 14 09 05 16605-16618 |
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10.1007/s11227-022-04522-3 doi (DE-627)OLC2079484338 (DE-He213)s11227-022-04522-3-p DE-627 ger DE-627 rakwb eng 004 620 VZ Zhao, Ying-Ze verfasserin aut Embedded connectivity of some BC networks 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. Embedded connectivity Fault-tolerance BC network Crossed cube Möbius cube Generalized product Li, Xiang-Jun (orcid)0000-0003-1194-1124 aut Ma, Meijie aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 14 vom: 09. Mai, Seite 16605-16618 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:14 day:09 month:05 pages:16605-16618 https://doi.org/10.1007/s11227-022-04522-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 14 09 05 16605-16618 |
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10.1007/s11227-022-04522-3 doi (DE-627)OLC2079484338 (DE-He213)s11227-022-04522-3-p DE-627 ger DE-627 rakwb eng 004 620 VZ Zhao, Ying-Ze verfasserin aut Embedded connectivity of some BC networks 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. Embedded connectivity Fault-tolerance BC network Crossed cube Möbius cube Generalized product Li, Xiang-Jun (orcid)0000-0003-1194-1124 aut Ma, Meijie aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 14 vom: 09. Mai, Seite 16605-16618 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:14 day:09 month:05 pages:16605-16618 https://doi.org/10.1007/s11227-022-04522-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 14 09 05 16605-16618 |
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10.1007/s11227-022-04522-3 doi (DE-627)OLC2079484338 (DE-He213)s11227-022-04522-3-p DE-627 ger DE-627 rakwb eng 004 620 VZ Zhao, Ying-Ze verfasserin aut Embedded connectivity of some BC networks 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. Embedded connectivity Fault-tolerance BC network Crossed cube Möbius cube Generalized product Li, Xiang-Jun (orcid)0000-0003-1194-1124 aut Ma, Meijie aut Enthalten in The journal of supercomputing Springer US, 1987 78(2022), 14 vom: 09. Mai, Seite 16605-16618 (DE-627)13046466X (DE-600)740510-8 (DE-576)018667775 0920-8542 nnns volume:78 year:2022 number:14 day:09 month:05 pages:16605-16618 https://doi.org/10.1007/s11227-022-04522-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 78 2022 14 09 05 16605-16618 |
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Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
abstractGer |
Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
abstract_unstemmed |
Abstract Many interconnection networks in large-scale parallel computing have hierarchical and recursive structures. The presence of vertex failures may disconnect the entire network, but every fault-free processor still lies in an undamaged sub-network, which is a smaller network with the same topological properties as the original one. For an n-dimensional recursive network $$G_{n}$$, the h-embedded connectivity $$\zeta _{h}$$ of $$G_{n}$$ is the minimum number of vertices whose removal disconnects $$G_n$$ and each vertex in the resulting network is contained in an h-dimensional undamaged sub-network. The bijective connection networks (BC networks for short) are a class of cube-based networks. They have recursive structures and contain many known networks, such as the hypercube, the Crossed cube, and the Möbius cube. This paper focuses on the structures of the Crossed cube and the Möbius cube. We prove that these two networks are generalized product graphs, using these results to determine the $$\zeta _{h}$$ of them for $$h\le n-2$$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 |
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title_short |
Embedded connectivity of some BC networks |
url |
https://doi.org/10.1007/s11227-022-04522-3 |
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author2 |
Li, Xiang-Jun Ma, Meijie |
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Li, Xiang-Jun Ma, Meijie |
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doi_str |
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up_date |
2024-07-04T01:05:53.415Z |
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