| Summary: | 碩士 === 靜宜大學 === 資訊工程學系 === 104 === For large-scale networking environments, grouping network nodes into clusters is a key technique to achieve the scalability objective. This thesis addresses cycle-based node clustering in network systems. Let r be a positive integer. For any r distinct vertices v_1 ,··· ,v_r of a network G= (V,E), G is said to be spanning (v_1 ,··· ,v_r)-cyclable if there exists a set of r vertex-disjoint cycles C_1,··· ,C_r in G such that min{l(C_1),···,l(C_r)}≥ 4, ∑_(i=1)^r▒〖C_i=|V|〗, and v_i ∈ V (C_i ) for 1 ≤ i ≤ r, where ℓ(Ci) denotes the length of cycle C_i, |V | is the total number of vertices in G, and V (C_i) denotes the set of vertices traversed by C_i. Naturally, C_1,···,C_r form a collection of r clusters indexed by cluster heads v_1 ,··· ,v_r. The matching composition network is a general family of network topologies, each of which connects two components with the same number of vertices by a perfect matching. Applying our proposed main theorem, indexing cycle-based clusters in many well-known matching composition networks can be done.
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