Sentence examples for a valid combination from inspiring English sources

Let { Γ a 1, Γ a p } be a valid combination in the optimum solution.

The searching for three-wise combinations similar to Algorithm 1 is as follows: We first search for a valid combination involving the largest element in U ′.

Inspired by Lemma 1, we may first find a valid pairwise combination involving the largest element in W. If such a valid combination is found, we can start looking at the second largest element in W and try to find a valid combination involving it.

There is an optimum solution for (20), where arg max i { Γ i | i ∈ W } is involved in a valid combination, if there exists at least one valid combination.

After receiving all the required network-coded packets correctly, the destination requests the relay for each of the packets that is neither involved in a valid combination nor received correctly.

Also, assume that { Γ a 1, Γ a q } is found as a valid pairwise combination by Algorithm 1. From Lemma 1, we know there is an optimum solution, where Γ a 1 is involved in a valid combination.

Let l = arg max i { Γ i | i ∈ W }. If there is an optimum solution that does not use l in any valid combination, then swapping l with any element involved in any valid combination found will not affect the optimality of the solution.

The details of the algorithm are the following: At the end of Algorithm 1, we can represent W as W = S 1 ⋃ S 2 ⋃... ⋃ S c ⋃ ℬ, where S i, i ∈ [ 1, t 1 ] is a set that contains indices of packets involved in a pairwise valid combination, and | S i | = 2, ℬ is the set that contains indices of packets not involved in any pairwise valid combination.

Consequentially, the square matrix on Table 1 represents all valid combinations of allocations, for a gene that is a member of two distinct biochemical pathways, giving rise to all possible hamming distances.

Let VC m be the number of m-wise valid combinations found, where m ∈ [2, ω ] (i.e., there exists a ω-wise valid combination that is formed by the sum of most SNRs among all valid combinations).

Let Γα,SD, Γβ,SD, and Γγ,SD form a three-wise valid combination and, in order to decode source packets, P α, P β, P γ, P i′, and P r′ should be retransmitted, where i, r∈[1,x].