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. Author manuscript; available in PMC: 2014 Jan 13.
Published in final edited form as: Inf inference. 2012 Dec;1(1):21. doi: 10.1093/imaiai/ias002

Algorithm 1.

Finding a WUL subgraph of a graph with four anchors or pseudo-anchors

Require: Simple graph G =(V, E) with n atoms, k anchors, and ε a small positive constant (e.g., 10−4).
1: Randomize a realization q1,…, qn in ℝ3 and compute the distances dij =∥qi − qj∥ for (i, j) ∈ E.
2: If k < 4, find a complete subgraph of G on 4 vertices (i.e., K4) and compute an embedding of it (using classical MDS) with distances dij computed in step 1. Denote the set of pseudo-anchors by 𝒜.
3: Solve the SDP relaxation problem formulated in (4.3) using the anchor set 𝒜 and the distances dij computed in step 1 above.
4: Denote by the vector w the diagonal elements of the matrix Y − XX⊤.
5: Find the subset of nodes V0 ∈ V\𝒜 such that wi < ε.
6: Denote G0 =(V0, E0) the weakly uniquely localizable subgraph of G.