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It is proven in this paper that the considered problem is strongly NP-complete even for node-weighted trees (the weight of each edge is 1) with one vertex of degree greater than 2. It is also shown that there exists a polynomial-time algorithm for finding an optimal connected search strategy for a given bounded degree tree with arbitrary weights on the edges and on the vertices.
In an edge-weighted tree, the weight of each edge is assigned to its corresponding split.
The pairwise similarity between any two groups is shown in Figure 2. Using this, one can construct a weighted graph where each vertex denotes a group and the weight of each edge equals to the similarity between two groups that are connected by this edge.
The weight of each edge is equal to one.
Result of the OWA aggregation specifies weight of each edge in the road network graph.
The weight of each edge tells how good this combination is.
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The weights of each edge in G (k)(V,E (k)) are concatenated to generate the k-th early fused similarity vector, denoted as (mathbf {X}^{ k)}=[X^{ k)}_{1},cdots,X^{ k)}_{N^{2}}]^{T}).
While C is the diagonal matrix with the weights of each edge along the diagonal, A is the incidence matrix indicating combinatorial gradients, and it can be defined as: A e ij v k = 1 if i = k − 1 if j = k 0 otherwise.
Within subjects, weights of each edge were normally distributed around the mean weights.
Given S, we let it be the set of edges D for computing the means and standard deviations of the spatial and feature differences that then determine normalized scores for d S and d A. For a series of different values of α>0, we then apply the bipartite matching heuristic where the weights of each edge are determined by D= S and α.
To solve it, we first build a directed graph by creating two directed edges with the same weight for each edge of G and create a source vertex connecting to the vertices in V select with weight ω select and a sink vertex connected from the vertices in V unselect with weight ω unselect.
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Justyna Jupowicz-Kozak
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