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The edge distance between two pseudogenization vertices a ψ and b ψ′ where a ψ, b ψ are origins of edges e a and e b, respectively, such that e a, e b ∈ E G ∗), is defined as the minimum length path between e a and e b in G ∗.
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In order to measure distances between vertices in a graph, we denote d u,v) as distance between u∈V and v∈V expressed as the minimum length of a path between u,v.
For each i, j ∈ { 1, …, I }, the distance d i, j between Nodes i and j is defined as the minimum length of a path joining these two nodes.
The degree (mathrm{d}_{v}) of (v in V) is the size of the neighborhood (|N v |) of v. Let (diam(G) = max_{v,u} D v,u)) denote the diameter of G defined as the longest shortest path between any two vertices (v, u) of G where D v, u) is the graph distance between v and u, i.e., the minimum length of the paths connecting them.
These are the minimum length of a C[ S]-path and path in the neutral network between s and s', respectively.
The objective of path planning for a mobile anchor is to find the path of minimum length that the anchor traverses to localize all sensors.
Furthermore, data is routed unblocked over paths with minimum length.
The purpose of this approach is to find collision free and feasible paths with minimum length and terrain roughness.
As expected, the Hop count metric selects the paths with minimum length in hops.
The classic version of the problem aims to find an obstacle-free path with the minimum length for a given workspace containing a set of obstacles and two sources and destination points.
However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com