Definitions and the Model Sample Clauses

Definitions and the Model. Definition 2. A hypergraph H is defined as the ordered pair (P, E) where P is a set of vertices and E ⊆ 2P is a monotone2 set of hyperedges. A set e ∈ E is called a |e|-hyperedge. The maximal basis of E is {e ∈ E| no proper superset of e is in E}. { } ∈ { } We model the network as a hypergraph H(P, E) where P = p1, p2,..., pn is the set of processes and p1, p2, ..., pk E if and only if p1, p2, ..., pk are connected by a local broadcast. Definition 3. A 3-uniform hypergraph is a hypergraph H(P, E) in which all hy- peredges in the maximal basis of E are 3-hyperedges. A (2, 3)-uniform hypergraph is a hypergraph H(P, E) in which every hyperedge in the maximal basis of E is either a 2-hyperedge or a 3-hyperedge. In this paper, we work with networks that are modeled by a (2, 3)-uniform hypergraph. Definition 4. If P1, P2,... , Pm are mutually disjoint non empty sets of size ≤( t such that P1 ∪ P2 ∪ ... ∪ Pm = P, then we say (P1, P2,..., Pm) forms a
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