Published in:
Journal on Computational Geometry and Applications, Volume 20, Number 6, December 2010, pp. 685-706.
A two-dimensional
mixed framework is a pair (G,p), where G=(V;D,L) is a graph whose
edges are labeled as `direction' or `length' edges, and a map
p from V to R^{2}.
The label of an edge uv represents a direction or length constraint
between p(u) and p(v). The framework (G,p) is called
globally rigid if every other framework (G,q) in which
the direction or length between the
endvertices of
corresponding
edges is the same
is `congruent' to (G,p), i.e. it can be obtained from (G,p) by
a translation and possibly by a dilation by -1.
We show that labeled versions of the two Henneberg operations
(0-extension and 1-extension)
preserve global rigidity of generic mixed frameworks. These results,
together with appropriate inductive constructions, can be
used to verify generic global rigidity of special families of
mixed graphs.
Bibtex entry:
@techreport{egres-08-08,
AUTHOR | = | {Jackson, Bill and Jord{\'a}n, Tibor}, |
TITLE | = | {Operations Preserving Global Rigidity of Generic Direction-Length Frameworks}, |
NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
YEAR | = | {2008}, |
NUMBER | = | {TR-2008-08} |