منابع مشابه
Expander Construction in VNC1
We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [38], and show that this analysis can be formalized in the bounded-arithmetic system VNC1 (corresponding to the “NC1 reasoning”). As a corollary, we prove the assumption made by Jeřábek [24] that a construction of certain bipartite expander graphs ca...
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We construct a sequence of groups Gn, and explicit sets of generators Yn ⊂ Gn, such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 is the alternating group Ad, the set of even permutations on the elements {1, 2, . . . , d}. The group Gn is the group of all even symmetries of the rooted d-regular tree of depth n. Our results hold for ...
متن کاملDistributed Construction of Random Expander Graphs
We present a novel distributed algorithm for constructing random regular graphs that are composed of d independent Hamilton cycles. The protocol is completely decentralized as no globally-known server is required. The constructed topologies are expanders with O(logd n) diameter with high probability. Our construction is highly scalable because both the processing and the space requirements at e...
متن کاملAn Explicit Construction of an Expander Family
This paper proves that there exist infinite families of graphs which satisfy a uniform lower bound on their spectral gap. We first prove existence via a probabilistic method. The explicit construction involves various results from algebra and representation theory, which we explore at some length. It turns out that the expander family we construct achieves a maximal condition on expander famili...
متن کاملDistributed Construction of Random Expander Networks
We present a novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles. The protocol is completely decentralized as no globally-known server is required. The constructed topologies are expanders with O(logd n) diameter with high probability. Our construction is highly scalable because both the processing and the space requirements at each node g...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2020
ISSN: 0168-0072
DOI: 10.1016/j.apal.2020.102796