SA and SB ); variable nodes of the same subgroup can take their canalyzing spin values simultaneously in state β , while variable nodes from different subgroups will never take their corresponding canalyzing spin values simultaneously in state β .
Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problem
Therefore, in some microscopic conﬁgurations, variable nodes in SA will take their canalyzing spin values; and in some other microscopic conﬁgruations, variable nodes in SB will take their canalyzing spin values.
Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problem
Clearly, |Sa | and |Db | are the degrees of nodes a ∈ S and b ∈ D in the conﬂict graph of step s.
Online Permutation Routing in Partitioned Optical Passive Star Networks
Since a similar result holds for every a ∈ S and b ∈ D, we also know that for every d > 0 (1 − d) |Sa |g ds ≤ S′a ≤ (1 + d)g, (1 − d) |Db |g ds ≤ D′b ≤ (1 + d)g, hold for every a ∈ S and b ∈ D, with probability at least 1 − 4ge−d2 g/4 , by the union bound over the 2g nodes of the conﬂict graph.
Online Permutation Routing in Partitioned Optical Passive Star Networks
According to the former analysis of MFPT, we know that the high-degree nodes would be visited early, so as to be avoided by SA walker preferentially.
Walks on Apollonian networks
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