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Motivated by the peer-to-peer content sharing systems in large-scale networks, we will study interval routing schemes in Erdös-Rényi random graphs. C. Gavoille and D. Peleg [13] posed an open question of whether almost all networks support a shortest-path interval routing scheme with 1 interval. In this paper, we answer this question partially by proving(More)
Emergence of dominating cliques in Erdös-Rényi random graph model G(n, p) is investigated in this paper. It is shown this phenomenon possesses a phase transition. Namely, we have argued that, given a constant probability p, an n-node random graph G from G(n, p) and for r = c log 1/p n with 1 ≤ c ≤ 2, it holds: (1) if p > 1/2 then an r-node clique is(More)
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