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Summary: Mathematical Programming manuscript No.
(will be inserted by the editor)
On Stress Matrices of (d + 1)-lateration Frameworks in
General Position
A. Y. Alfakih · Nicole Taheri · Yinyu Ye
Received: date / Accepted: date
Abstract Let (G, P) be a bar framework of n vertices in general position in
Rd
, for d n - 1, where G is a (d + 1)-lateration graph. In this paper, we
present a constructive proof that (G, P) admits a positive semidefinite stress
matrix with rank (n-d-1). We also prove a similar result for a sensor network,
where the graph consists of m( d + 1) anchors.
Mathematics Subject Classification (2000) 52C25 · 05C62 · 15A57 ·
90C22
Keywords Universal Rigidity · Stress Matrices · General Position ·
Semidefinite Programming
1 Introduction
Let V (G) and E(G) be, respectively, the vertex set and the edge set of a simple
edge-weighted graph G, where each edge (i, j) has a positive weight dij. The
graph realization problem (GRP) is the problem of determining whether there
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