Steven Karger (1959–2008)

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Graph Coloring ( 1994 , 1998 ; Karger , Motwani , Sudan )

An independent set in an undirected graph G = (V,E) is a set of vertices that induce a subgraph which does not contain any edges. The size of the maximum independent set in G is denoted by α(G). For an integer k, a k-coloring of G is a function σ : V → [1 . . . k] which assigns colors to the vertices of G. A valid k-coloring of G is a coloring in which each color class is an independent set. Th...

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My main interest is analytic number theory and random matrix theory (especially the distribution of zeros of L-functions and the eigenvalues of random matrix ensembles); I am also studying equidistribution problems in analysis and probability, and working on applied problems in probability, statistics, graph theory, cryptography, sabermetrics and linear programming where the tools and technique...

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Lecture 2 : Karger ’ s Min Cut Algorithm

(These notes are a slightly modified version of notes from previous offerings of the class scribed by Sanjeev.) Today’s topic is simple but gorgeous: Karger’s min cut algorithm and its extension. It is a simple randomized algorithm for finding the minimum cut in a graph: a subset of vertices S in which the set of edges leaving S, denoted E(S, S) has minimum size among all subsets. You may have ...

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on Karger ’ s Min - Cut Algorithm

Traditionally, the min-cut problem was solved by solving n − 1 min-st-cut problems. In the min-st-cut problem we are given as input two vertices s and t, our aim is to find the set S where s ∈ S and t / ∈ S which minimizes the size of the cut (S, S), i.e., |δ(S)|. The size of the min-st-cut is equal to the value of the max-st-flow (equivalent by linear programming duality). The fastest algorith...

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Steven Buechler

Geometrical stability theory is a powerful set of model-theoretic tools that can lead to structural results on models of a simple first-order theory. Typical results offer a characterization of the groups definable in a model of the theory. The work is carried out in a universal domain of the theory (a saturated model) in which the Stone space topology on ultrafilters of definable relations is ...

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ژورنال

عنوان ژورنال: Cardiology

سال: 2008

ISSN: 0008-6312,1421-9751

DOI: 10.1159/000127594