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If both proteins in every pair in M have similar evolutionary histories, then we say that M forms a match of size k.
This relationship does not hold in general in the opposite direction - an MMM match of size k > 3 is not necessarily an MMMvII match.
This is in contrast with MMMvII which provides an elementary definition for matches of size greater than 3 that does not recursively depend on the definition of a match of size 3.
However, for a set of k > 3 protein pairs, MMM takes every possible triplet of pairs from that set and tests if it forms a match of size 3.
In the ideal case, if M is a match of size k then all k-choose-2 RPDs would have the same value, indicating that the A distances are a scaled copy of their paired B distances.
As an example, consider two triplets of proteins: { a2, a3, a5} ⊆ A and { b3, b7, b8} ⊆ B, with corresponding phylogenetic distances d1 through d6, as depicted in Figure 2. If d1/ d4 ≈ d2/ d5 ≈ d3/ d6, under a given α, then we consider the set of protein pairs { a2, b3), (a3, b7), (a5, b8)} to form a match of size 3, with each pair representing two coevolving proteins.
Similar(54)
For a given graph and number, KVMP is a decision process that determines whether has a -valid matching of size.
For, leache the subgraph subset of such that all edges in are of the form for some.
Thus, whether the set of edges constitute a -valid matching of size with a total weight of can be verified in polynomial time.
Definition 2. For a given graph, number, and weight, WKVMP is a decision process that determines whether has a -valid matching of size and total weight.
Such a design can be represented as a square array whose cells are either empty or contain a matching of size k, where every vertex appears exactly once in each row and column.
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