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Fig. 5 | EURASIP Journal on Advances in Signal Processing

Fig. 5

From: Backtracking-based dynamic programming for resolving transmit ambiguities in WSN localization

Fig. 5

Illustration of a tree node s and its vertex set \(\mathcal {V}_{s}\), which is used to visualize R s (v) for the two vertices vi,j(l,r) and v i ,j(l,r). The corresponding vertex sets for vi,j(l,r) are \(\mathcal {V}_{1,a}(i,l)\), \(\mathcal {V}_{1,b}(j,r)\), and \(\mathcal {V}_{2}(i,j)\) and are indicated by dashed contours. The sets \(\mathcal {V}_{1,a}(i',l')\), \(\mathcal {V}_{1,b}(j,r)\), and \(\mathcal {V}_{2}(i',j)\) for v i ,j(l,r) are shown with dotted contours. The set \(\mathcal {V}_{1,b}(j,r)\), which is considered for both vertices, therefore has a dash-dotted contour. The purpose of visualizing R s (v) for the two vertices is to check whether all vertices of the abovementioned sets \(\mathcal {V}_{\bullet }(\bullet,\bullet)\) are already included in the vertex set \(\mathcal {V}_{s}\) at the current tree node s. For the two vertices in the example above, we have R s (vi,j(l,r)) = ((0,0),(j,r),(0,0))=R s (v i ,j(l,r)) because for both vertices, the corresponding set \(\mathcal {V}_{1,b}(\bullet,\bullet)\) is not fully included in \(\mathcal {V}_{s}\). Consequently, both vertices share the same property, which is captured by R s (vi,j(l,r))=R s (v i ,j(l,r)). Therefore, they also have the same label (color)

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