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We give a random class of lattices in Z n so that, if there is a probabilistic polynomial time algorithm which nds a short vector in a random lattice with a probability of at least 1 2 then there is also a probabilistic polynomial time algorithm which solves the following three lattice problems in every lattice in Z n with a probability exponentially close(More)
Let G be a (k + I)-graph (a hypergraph with each hyperedge of size k + 1) with n vertices and average degree t. Assume k Q t Q n. If G is uncrowded (contains no cycle of size 2, 3, dr 4) then there exists an independent set of size c,(n/t)(ln t)'lk. Let G be a graph with n vertices and average valence t. Turan's theorem implies a(G) > n/(t + 1). (See(More)