Article
NearlyLinear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems
SIAM Journal on Matrix Analysis and Applications (Impact Factor: 1.81). 07/2006; DOI: 10.1137/090771430
Source: arXiv

Article: Trend Filtering on Graphs
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ABSTRACT: We introduce a family of adaptive estimators on graphs, based on penalizing the $\ell_1$ norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate nonparametric regression, to graphs. Analogous to the univariate case, graph trend filtering exhibits a level of local adaptivity unmatched by the usual $\ell_2$based graph smoothers. It is also defined by a convex minimization problem that is readily solved (e.g., by fast ADMM or Newton algorithms). We demonstrate the merits of graph trend filtering through examples and theory.10/2014; 
Conference Paper: Constructing smallsignal equivalent impedances using ellipsoidal norms
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ABSTRACT: Analysis of VLSI designs and circuits often requires the construction of a smallsignal equivalent impedance representation between prescribed node pairs. Examples include IRdrop calculation, electrical overstress verification, ESD protection, di/dt current rush analysis, electromigration checks, thermal analysis and model order reduction. VLSI designs consisting of hundreds of millions (10e11) of linear circuit elements are now commonplace and thus any method which requires compute intensive calculations is difficult to apply for all the elements of the circuit. By definition, given a circuit with n elements, conventional analysis techniques have a Ω(η2) lowerbound to exhaustively enumerate all nodepairs which meet a constraint criteria. We present the first 0(nlgn + k) algorithm for answering queries of the form: ∃(x, y):((x, y) ϵ × n) ∧(Zeff (x, y) <; Z) where Zeff(x, y) is the equivalent impedance between nodes x and y, and k nodepairs meet the constraint. Calculating all node pairs for which these constraints are met is compute intensive using existing techniques, even using heuristic methods. In this paper a new technique based on method of projection using ellipsoidal norms is presented. Our proposed method employs recently discovered techniques from theoretical computer science to compute an eapproximate embedding matrix from which effective impedance of all node pairs can be estimated as easily as taking the Euclidean norm of column differences. Using computational geometry methods, existence queries can then be answered in logarithmic time. The method works for general circuits containing resistances, capacitances, and inductances.2014 15th International Symposium on Quality Electronic Design (ISQED); 03/2014  [Show abstract] [Hide abstract]
ABSTRACT: We show a closer algorithmic connection between constructing cutapproximating hierarchical tree decompositions and computing approximate maximum flows in undirected graphs. This leads to the first O(m polylog(n)) time algorithms for both problems.11/2014;
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