Christian Borgs

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Diffusion is a fundamental graph process, underpinning such phenomena as epidemic disease contagion and the spread of innovation by word-of-mouth. We address the algorithmic problem of finding a set of k initial seed nodes in a network so that the expected size of the resulting cascade is maximized, under the standard independent cascade model of network(More)
We consider sequences of graphs (Gn) and define various notions of convergence related to these sequences: “left convergence” defined in terms of the densities of homomorphisms from small graphs into Gn; “right convergence” defined in terms of the densities of homomorphisms from Gn into small graphs; and convergence in a suitably defined metric. In Part I(More)
We consider sequences of graphs (Gn) and define various notions of convergence related to these sequences including “left convergence,” defined in terms of the densities of homomorphisms from small graphs into Gn, and “right convergence,” defined in terms of the densities of homomorphisms from Gn into small graphs. We show that right convergence is(More)
We consider the random 2-satisfiability problem, in which each instance is a formula that is the conjunction of m clauses of the form x∨ y, chosen uniformly at random from among all 2-clauses on n Boolean variables and their negations. As m and n tend to infinity in the ratio m/n → α, the problem is known to have a phase transition at αc = 1, below which(More)
We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has fractional solution then BP(More)
High-quality, personalized recommendations are a key feature in many online systems. Since these systems often have explicit knowledge of social network structures, the recommendations may incorporate this information. This paper focuses on networks that represent trust and recommendation systems that incorporate these trust relationships. The goal of a(More)
Motivated by the problem of detecting link-spam, we consider the following graph-theoretic primitive: Given a webgraph G, a vertex v in G, and a parameter δ ∈ (0, 1), compute the set of all vertices that contribute to v at least a δ fraction of v’s PageRank. We call this set the δ-contributing set of v. To this end, we define the contribution vector of v to(More)
A well-known result in game theory known as "the Folk Theorem" suggests that finding Nash equilibria in repeated games should be easier than in one-shot games. In contrast, we show that the problem of finding any (approximate) Nash equilibrium for a three-player infinitely-repeated game is computationally intractable (even when all payoffs are in {-1,0,1}),(More)