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The adoption of everyday decisions in public affairs, fashion, movie-going, and consumer behavior is now thoroughly believed to migrate in a population through an influential network. The same diffusion process when being imitated by intention is called viral marketing. This process can be modeled by a (directed) graph G = (V, E) with a threshold t(v) for… (More)

We show that the number of maximal sum-free subsets of {1, 2,. .. , n} is at most 2 3n/8+o(n). We also show that 2 0.406n+o(n) is an upper bound on the number of maximal product-free subsets of any group of order n.

We consider the next random process for generating a maximal H-free graph: Given a fixed graph H and an integer n, start by taking a uniformly random permutation of the edges of the complete n-vertex graph K n. Then, traverse the edges of K n according to the order imposed by the permutation and add each traversed edge to an (initially empty) evolving… (More)

Consider the triangle-free process, which is defined as follows. Start with G(0), an empty graph on n vertices. Given G(i − 1), let G(i) = G(i − 1) ∪ {g(i)}, where g(i) is an edge that is chosen uniformly at random from the set of edges that are not in G(i − 1) and can be added to G(i − 1) without creating a triangle. The process ends once a maximal… (More)

We investigate derandomizations of digital good randomized auctions. We propose a general derandomization method which can be used to show that for every random auction there exists a deterministic auction having asymptotically the same revenue. In addition, we construct an explicit optimal deterministic auction for bi-valued auctions.

Let A be a randomized, unlimited supply, unit demand, single-item auction, which given a bid-vector b ∈ [h] n , has expected profit E[P (b)]. Aggarwal et al. showed that given A, there exists a de-terministic auction which given a bid-vector b, guarantees a profit of E[P (b)]/4 − O(h). In this paper we show that given A, there exists a deterministic auction… (More)

Let X be the random variable that counts the number of triangles in the random graph G(n, p). We show that for some absolute constant c, the probability that X deviates from its expectation by at least λ Var(X)