Cycle Embedding in Folded Hypercubes with More Faulty Elements
نویسندگان
چکیده
Faults in a network may take various forms such as hardware/software errors, vertex/edge faults, etc. Folded hypercube is a well-known variation of the hypercube structure and can be constructed from a hypercube by adding a link to every pair of nodes with complementary addresses. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. have shown that FQn − FFv − FFe for n ≥ 3 contains a fault-free cycle of length at least 2 − 2|FFv|, under the constraints that (1) |FFv| + |FFe| ≤ 2n − 4 and (2) every node in FQn is incident to at least two fault-free links. In this paper, we further consider the constraints |FFv|+ |FFe| ≤ 2n− 3. We prove that FQn − FFv − FFe for n ≥ 5 still has a fault-free cycle of length at least 2 − 2|FFv|, under the constraints : (1) |FFv|+ |FFe| ≤ 2n− 3, (2) |FFe| ≥ n+ 2, and (3) every vertex is still incident with at least two links. Keywords—Folded hypercubes; Interconnection networks; Cycle embedding; Faulty elements.
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