Characterizing redundant rigidity and redundant global rigidity of body-hinge graphs
In this paper, we characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity. Although an efficient algorithm which determines mixed-connectivity is still not known, our result implies that both edge-redundancy for rigidity and edg...
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| Published in | Information processing letters Vol. 116; no. 2; pp. 175 - 178 |
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| Format | Journal Article |
| Language | English |
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Elsevier B.V
01.02.2016
Elsevier Sequoia S.A |
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| Abstract | In this paper, we characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity.
Although an efficient algorithm which determines mixed-connectivity is still not known, our result implies that both edge-redundancy for rigidity and edge-redundancy for global rigidity can be checked via efficient graph-connectivity algorithms.
•We characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity.•Our result implies that both edge-redundancy for rigidity and edge-redundancy for global rigidity can be checked via efficient graph-connectivity algorithms.•Our result is contrasted with the fact that the problem of augmenting a Laman graph (i.e., the graph corresponding to a minimally rigid generic bar-joint framework in 2-dimension) to a 2-edge-rigid bar-joint graph with a minimum number of added edges is NP-hard. |
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| AbstractList | In this paper, we characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity.
Although an efficient algorithm which determines mixed-connectivity is still not known, our result implies that both edge-redundancy for rigidity and edge-redundancy for global rigidity can be checked via efficient graph-connectivity algorithms.
•We characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity.•Our result implies that both edge-redundancy for rigidity and edge-redundancy for global rigidity can be checked via efficient graph-connectivity algorithms.•Our result is contrasted with the fact that the problem of augmenting a Laman graph (i.e., the graph corresponding to a minimally rigid generic bar-joint framework in 2-dimension) to a 2-edge-rigid bar-joint graph with a minimum number of added edges is NP-hard. In this paper, we characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity. Although an efficient algorithm which determines mixed-connectivity is still not known, our result implies that both edge-redundancy for rigidity and edge-redundancy for global rigidity can be checked via efficient graph-connectivity algorithms. |
| Author | Kobayashi, Yuki Katoh, Naoki Higashikawa, Yuya Sljoka, Adnan |
| Author_xml | – sequence: 1 givenname: Yuki surname: Kobayashi fullname: Kobayashi, Yuki email: kobayashi.y.bv@m.titech.ac.jp organization: Department of Architecture, Tokyo Institute of Technology, Japan – sequence: 2 givenname: Yuya surname: Higashikawa fullname: Higashikawa, Yuya organization: Department of Information and System Engineering, Chuo University, Japan – sequence: 3 givenname: Naoki surname: Katoh fullname: Katoh, Naoki organization: Department of Informatics, Kwansei Gakuin University, Japan – sequence: 4 givenname: Adnan orcidid: 0000-0002-2398-9523 surname: Sljoka fullname: Sljoka, Adnan organization: Department of Informatics, Kwansei Gakuin University, Japan |
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| Keywords | Edge-connectivity Redundant rigidity Algorithms Mixed-connectivity Combinatorial rigidity Global rigidity Body-hinge graph |
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| Snippet | In this paper, we characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity.
Although an... In this paper, we characterize the redundant rigidity and the redundant global rigidity of body-hinge graphs in Rd in terms of graph connectivity. Although an... |
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| SubjectTerms | Algorithms Body-hinge graph Combinatorial rigidity Connectivity Edge-connectivity Global rigidity Graphs Mixed-connectivity Redundant rigidity Studies |
| Title | Characterizing redundant rigidity and redundant global rigidity of body-hinge graphs |
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