Characterization of the Congestion Lemma on Layout Computation
An embedding of a guest network GN into a host network HN is to find a suitable bijective function between the vertices of the guest and the host such that each link of GN is stretched to a path in HN. The layout measure is attained by counting the length of paths in HN corresponding to the links in...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2984703 |
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| author | Jia-Bao Liu Arul Jeya Shalini Micheal Arockiaraj J. Nancy Delaila |
| author_facet | Jia-Bao Liu Arul Jeya Shalini Micheal Arockiaraj J. Nancy Delaila |
| author_sort | Jia-Bao Liu |
| collection | DOAJ |
| description | An embedding of a guest network GN into a host network HN is to find a suitable bijective function between the vertices of the guest and the host such that each link of GN is stretched to a path in HN. The layout measure is attained by counting the length of paths in HN corresponding to the links in GN and with a complexity of finding the best possible function overall graph embedding. This measure can be computed by summing the minimum congestions on each link of HN, called the congestion lemma. In the current study, we discuss and characterize the congestion lemma by considering the regularity and optimality of the guest network. The exact values of the layout are generally hard to find and were known for very restricted combinations of guest and host networks. In this series, we derive the correct layout measures of circulant networks by embedding them into the path- and cycle-of-complete graphs. |
| format | Article |
| id | doaj-art-12fe8b2e16f644a581f9346d661dca59 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-12fe8b2e16f644a581f9346d661dca592025-08-20T02:01:42ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/2984703Characterization of the Congestion Lemma on Layout ComputationJia-Bao Liu0Arul Jeya Shalini1Micheal Arockiaraj2J. Nancy Delaila3School of Mathematics and PhysicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsAn embedding of a guest network GN into a host network HN is to find a suitable bijective function between the vertices of the guest and the host such that each link of GN is stretched to a path in HN. The layout measure is attained by counting the length of paths in HN corresponding to the links in GN and with a complexity of finding the best possible function overall graph embedding. This measure can be computed by summing the minimum congestions on each link of HN, called the congestion lemma. In the current study, we discuss and characterize the congestion lemma by considering the regularity and optimality of the guest network. The exact values of the layout are generally hard to find and were known for very restricted combinations of guest and host networks. In this series, we derive the correct layout measures of circulant networks by embedding them into the path- and cycle-of-complete graphs.http://dx.doi.org/10.1155/2021/2984703 |
| spellingShingle | Jia-Bao Liu Arul Jeya Shalini Micheal Arockiaraj J. Nancy Delaila Characterization of the Congestion Lemma on Layout Computation Journal of Mathematics |
| title | Characterization of the Congestion Lemma on Layout Computation |
| title_full | Characterization of the Congestion Lemma on Layout Computation |
| title_fullStr | Characterization of the Congestion Lemma on Layout Computation |
| title_full_unstemmed | Characterization of the Congestion Lemma on Layout Computation |
| title_short | Characterization of the Congestion Lemma on Layout Computation |
| title_sort | characterization of the congestion lemma on layout computation |
| url | http://dx.doi.org/10.1155/2021/2984703 |
| work_keys_str_mv | AT jiabaoliu characterizationofthecongestionlemmaonlayoutcomputation AT aruljeyashalini characterizationofthecongestionlemmaonlayoutcomputation AT michealarockiaraj characterizationofthecongestionlemmaonlayoutcomputation AT jnancydelaila characterizationofthecongestionlemmaonlayoutcomputation |