Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Class of Minimal Generically Universally Rigid Frameworks   Following a review of related results in rigidity theory, we provide a
construction to obtain generically universally rigid frameworks with the
minimum number of edges, for any given set of n nodes in two or three
dimensions. When a set of edge-lengths is compatible with only one
configuration in d-dimensions, the framework is globally rigid. When that
configuration is unique even if embedded in a higher dimensional space, the
framework is universally rigid. In case of generic configurations, where the
nodal coordinates are algebraically independent, the minimum number of edges
required is equal to dn-d(d+1)/2+1, that is, 2n-2 for d=2, and 3n-5 for d=3.
Our contribution is a specific construction for this case by introducing a
class of frameworks generalizing that of Gr\"{u}nbaum polygons. The
construction applies also to nongeneric configurations, although in this case
the number of edges is not necessarily the minimum. One straightforward
application is the design of wireless sensor networks or multi-agent systems
with the minimum number of communication links.

28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph