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It is followed by an estimation of the capacity for each maximal clique in the contention graph.

The definition of a maximal clique is as follows: A maximal clique in a graph G is a clique not contained by any other clique in G.

Finding an SCC in (mathcal{G} ) is equivalent to finding a maximal clique in (S_{mathcal{G}} ), the strong connectivity graph of (mathcal{G} ).

At first sight, Algorithm 1, involves a computationally hard problem, since the problem of finding a maximal clique in a graph is known to be NP-complete [33].

Directly from the definitions of strong reachability, SCC and maximal clique, we see that the SCC in ({mathcal{G}}) is equivalent to finding the maximal clique in (S_{mathcal{G}}).

The authors used a contention graph to model the contention situation in a multihop network, and they presented an analytical model to estimate the capacity for each maximal clique in the contention graph.

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CliXO with dynamic checking for maximality and informativeness can compute all informative maximal cliques in O(Mnγ) where M is the number of non-zero edges in M, n = | T| and γ is the number of informative cliques in the final output G. Practically, γ ≪ μ, where μ is the total number of all maximal cliques at each unique t in U, and this results in significant performance increase.

In other words, the problem of maximizing probability for all non-critical receivers is equivalent to finding all the maximal cliques in the non-critical subgraph (mathcal {G}_{b}^{1:ell } kappa _{c}^)) and selecting the maximal clique among them that results in the maximum probability.

The problem of maximal clique enumeration (MCE) is to enumerate all of the maximal cliques in a graph.

Even the most efficient serial MCE algorithms require large amounts of time to enumerate the maximal cliques in networks arising from these problems that contain hundreds, thousands, or larger numbers of vertices.

Obviously, all the maximal cliques in G are contained in the set of the resulting cliques.

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