Characterizing redundant rigidity and redundant global rigidity of body-hinge graphs

• Published in: Information processing letters Vol. 116; no. 2; pp. 175 - 178
• Main Authors: Kobayashi, Yuki, Higashikawa, Yuya, Katoh, Naoki, Sljoka, Adnan
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2016; Elsevier Sequoia S.A
• Subjects: Algorithms; Body-hinge graph; Combinatorial rigidity; Connectivity; Edge-connectivity; Global rigidity; Graphs; Mixed-connectivity; Redundant rigidity; Studies; Edge-connectivity; Redundant rigidity; Algorithms; Mixed-connectivity; Combinatorial rigidity; Global rigidity; Body-hinge graph
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/j.ipl.2015.08.011

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.