Graph rigidity via Euclidean distance matrices |
| |
Authors: | AbdoY. Alfakih |
| |
Affiliation: | DepartmentofCombinatoricsandOptimization,UniversityofWaterloo, Waterloo,Ont., Canada N2L 3G1 |
| |
Abstract: | Let G=(V,E,ω) be an incomplete graph with node set V, edge set E, and nonnegative weights ωij's on the edges. Let each edge (vi,vj) be viewed as a rigid bar, of length ωij, which can rotate freely around its end nodes. A realization of a graph G is an assignment of coordinates, in some Euclidean space, to each node of G. In this paper, we consider the problem of determining whether or not a given realization of a graph G is rigid. We show that each realization of G can be epresented as a point in a compact convex set ; and that a generic realization of G is rigid if and only if its corresponding point is a vertex of Ω, i.e., an extreme point with full-dimensional normal cone. |
| |
Keywords: | Weighted graphs Rigidity Euclidean distance matrices Convex sets Normal cones Semidefinite programming |
本文献已被 ScienceDirect 等数据库收录! |
|