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Let be the clique with maximum weight in the subgraph which only contains vertices of and let be the weight of clique.
Because the MIS scheme selects the particle with maximum weight in the local distribution, the MIS procedure can be implemented sequentially.
However, max-max pairing is significantly computationally less expensive than optimal pairing as it is uses simpler comparison operations to search for the maximum weight in a single iteration.
By comparing the weight of the clique without including and the weight of the clique including, the clique with maximum weight in the subgraph including vertices in is set to be the one with the larger weight.
For Juglans and Morus, with very similar curves, after finishing the previous pollen season, the weight of current meteorological elements is higher reaching the maximum weight in early July, while afterwards the difference practically disappears (Figure 3, 4th panel from above, left and right).
Therefore, when the maximum weight is in the main particle region, the propagation process is achieved according to Eq. 23); on the other hand, when the maximum region is one of the sub-particle sets, the dynamic model changes to the following: {s}_t={As}_{t-1}^{mathrm{max}}+{B}_t{omega}_{t-1} (26)where ( {s}_{t-1}^{mathrm{max}} ) is the one that has the maximum weight in Eq. (24).
Similar(46)
In other words, the optimal packet combination (kappa _{i}^) that device i can generate in the nth transmission is the maximum weight clique in (mathcal {G}_{i}) in which the weights of vertices are defined in (15).
A mathematical description of the optimization problem is to find a minimum (or maximum) weight matching in a complete weighted bipartite graph.
In contrast, the maximum weight loss in the 4 mg/L was 8.3 ± 2.9% at day 3 and 7.5 ± 2.3% at day 3 in the control group (Fig. 3).
The optimal packet combination (kappa _{i}^) device i that can generate in the nth transmission to minimize the maximum delay is the maximum weight clique in its local IDNC graph (mathcal {G}_{i}) in which the weight of a vertex v jk is the following: begin{array}{*{20}l} w_{jk}^ =left{ begin{array}{ll} -log(p_{ij}) &qquad text{if}~ j in mathcal{L}(n) 0 & qquadtext{otherwise} end{array}right.
In this paper, we present coarse grained parallel graph algorithms with small message overheads that solve the following standard graph problems related to graph matching: finding maximum matchings in convex bipartite graphs, and finding maximum weight matchings in trees.
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