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We introduce a novel game that models the creation of Internet-like networks by selfish node-agents without central design or coordination. Nodes pay for the links that they establish, and benefit from short paths to all destinations. We study the Nash equilibria of this game, and prove results suggesting that the "price of anarchy" [4] in this context (the… (More)

We study the survey propagation algorithm [19, 5, 4], which is an iterative technique that appears to be very effective in solving random <i>k</i>-SAT problems even with densities close to threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number ρ. We then show… (More)

— We describe message-passing and decimation approaches for lossy source coding using low-density generator matrix (LDGM) codes. In particular, this paper addresses the problem of encoding a Bernoulli(¡) source: for randomly generated LDGM codes with suitably irregular degree distributions, our methods yield performance very close to the rate distortion… (More)

Two graphs with adjacency matrices <b>A</b> and <b>B</b> are isomorphic if there exists a permutation matrix <b>P</b> for which the identity <b>P</b><sup>T</sup><b>AP</b> = <b>B</b> holds. Multiplying through by <b>P</b> and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional… (More)

Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms , heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and connectivity of the solution space. Motivated by this work, we study structural and connectivity-related properties of… (More)

We study the structure of satisfying assignments of a random 3-Sat formula. In particular, we show that a random formula of density α ≥ 4.453 almost surely has no non-trivial " core " assignments. Core assignments are certain partial assignments that can be extended to satisfying assignments, and have been studied recently in connection with the Survey… (More)

—We study the use of low-density generator matrix (LDGM) codes for lossy compression of the Bernoulli symmetric source. First, we establish rigorous upper bounds on the average distortion achieved by check-regular ensemble of LDGM codes under optimal minimum distance source encoding. These bounds establish that the average distortion using such bounded… (More)

We provide a new characterization of convex geometries via a multivariate version of an identity that was originally proved, in a special case arising from the k-SAT problem, by Maneva, Mossel and Wainwright. We thus highlight the connection between various characterizations of convex geometries and a family of removal processes studied in the literature on… (More)

— We consider the problem of positioning data collecting base stations in a sensor network. We show that in general, the choice of positions has a marked influence on the data rate, or equivalently, the power efficiency, of the network. In our model, which is partly motivated by an experimental environmental monitoring system, the optimum data rate for a… (More)

We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as the length of the code goes to infinity via recent results in random hypergraphs [2]. For a code of finite length, we… (More)