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There may exist maximal matching of various sizes for the vertices of a graph; but, every maximal matching need not be a maximum matching; on the other hand, a maximum matching of the vertices in a graph is the largest possible maximal matching for the vertices of the graph.
We want to determine a maximal matching (need not be the maximum matching, but close enough to the maximum matching) of the vertices that are very similar to each other (or very dissimilar from each other).
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Figures 5, 6, 7, 8, 9 and 10 illustrate the maximal matching obtained for each of the real-world network graphs with respect to both maximal node matching and maximal assortative matching.
Using a novel model for the dynamics of maximal matching algorithms, we show that modified maximal matching algorithms guarantee stability of the switch and establish bounds on the average delay experienced by a packet.
Per definition, this results in a maximal matching.
What is left is your maximal matching.
The MAM algorithm has to be only slightly modified to determine an MDM: instead of preferring to include edges with a lower assortative weight (to maximize the assortative index of the maximal matching), we need to include the uncovered edge with the largest assortative weight (to minimize the assortative index of the maximal matching) in each iteration.
A maximal matching that is arbitrary with respect to the weight of the vertices being matched need not be preferred in social networks.
The more useful measure is probably maximal ATP production, which has been shown to be reduced in sepsis [ 92], indicating that the failure of production to match needs is a likely factor.
Algorithm 1 BuildPrefixArray build the positional prefix array from a k create empty arrays for do if then else the concatenation of a followed by b create empty arrays for do if then else the concatenation of a followed by b To identify where maximal matches start, we need to keep track of the start position of matches between neighboring prefixes.
We define the problem of maximal assortativity matching (MAM) as a variant of the maximal matching problem wherein we want to maximize the similarity between the end vertices (with respect to any particular measure for node weight) constituting the matching.
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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