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Existing techniques have been designed to detect shared congestion between a pair of paths with a common source or destination point.
For each such pair of paths P and P′ we can check whether points in the corresponding composite rectangle are scattered around a certain 45° line using SPAdes distance estimation procedure (Nurk et al., 2013).
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The look-up table related a pair of projection values (e.g., g H and g L ) at high and low energy spectra to a pair of path lengths of basis materials (e.g., d1 and d2).
It is obvious that not all pairs of paths lead to the same throughput.
After all paths are constructed, we consider all pairs of paths that form composite rectangles with non-zero number of points (Fig. 7).
However, for performance issues, the Velvet version of TourBus only visits each node once, meaning that it does not exhaustively compare all possible pairs of paths.
Alternatively, a graph kernel can also explicitly summarize the similarity between the shortest paths in the two graphs with each pair of shortest paths measured by a convolution kernel [ 110].
The shortest path from S to S ′ is found in PATH list as S−3−D−D ′−1−S ′ which has the least distance by using Algorithm 2. Ultimately, a pair of disjoint paths are found as S−3−D and S−1−D, their multi-path SHM is 0 and C is 1, which meets the requirement of Problem 1. Fig. 5 The example of algorithm.
For every pair of successive paths, we calculated the nearest-neighbour distance (NND) from every point on the first path to its closest neighbouring point on the second path.
Therefore, selecting any pair of alternate paths will not always result in improved throughput.
Intuitively, given two input sets of vertices X and Y, the desired bonding agents are the minimum set of vertices to remove in order to enlarge every pair of shortest path distance between X and Y.
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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