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Hypergraph Sparsification and Its Application to Partitioning
"... Abstract—The data one needs to cope to solve today’s problems is large scale, so are the graphs and hypergraphs used to model it. Today, we have BigData, big graphs, big matrices, and in the future, they are expected to be bigger and more complex. Many of today’s algorithms will be, and some already ..."
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already are, expensive to run on large datasets. In this work, we analyze a set of efficient techniques to make “big data”, which is modeled as a hypergraph, smaller so that its processing takes much less time. As an application use case, we take the hypergraph partitioning problem, which has been
Face Recognition: A Literature Survey
, 2000
"... ... This paper provides an uptodate critical survey of still and videobased face recognition research. There are two underlying motivations for us to write this survey paper: the first is to provide an uptodate review of the existing literature, and the second is to offer some insights into ..."
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Cited by 1363 (21 self)
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... This paper provides an uptodate critical survey of still and videobased face recognition research. There are two underlying motivations for us to write this survey paper: the first is to provide an uptodate review of the existing literature, and the second is to offer some insights into the studies of machine recognition of faces. To provide a comprehensive survey, we not only categorize existing recognition techniques but also present detailed descriptions of representative methods within each category. In addition,
Nearlylinear time algorithms for graph partitioning, graph sparsification, and solving linear systems (Extended Abstract)
 STOC'04
, 2004
"... We present algorithms for solving symmetric, diagonallydominant linear systems to accuracy ɛ in time linear in their number of nonzeros and log(κf (A)/ɛ), where κf (A) isthe condition number of the matrix defining the linear system. Our algorithm applies the preconditioned Chebyshev iteration with ..."
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Cited by 223 (11 self)
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with preconditioners designed using nearlylinear time algorithms for graph sparsification and graph partitioning.
On the Limits of Sparsification ⋆
"... Abstract. Impagliazzo, Paturi and Zane (JCSS 2001) proved a sparsification lemma for kCNFs: every kCNF is a subexponential size disjunction of kCNFs with a linear number of clauses. This lemma has subsequently played a key role in the study of the exact complexity of the satisfiability problem. ..."
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Cited by 2 (0 self)
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Abstract. Impagliazzo, Paturi and Zane (JCSS 2001) proved a sparsification lemma for kCNFs: every kCNF is a subexponential size disjunction of kCNFs with a linear number of clauses. This lemma has subsequently played a key role in the study of the exact complexity of the satisfiability problem
Extensions and Limits to Vertex Sparsification
"... Suppose we are given a graph G = (V, E) and a set of terminals K ⊂ V. We consider the problem of constructing a graph H = (K, EH) that approximately preserves the congestion of every multicommodity flow with endpoints supported in K. We refer to such a graph as a flow sparsifier. We prove that there ..."
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Cited by 16 (2 self)
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, EH) (a cut sparsifier) that approximately preserves the value of minimum cuts separating any partition of the terminals. Indirectly our result also allows us to give a construction for better quality cut sparsifiers (and flow sparsifiers). Thereby, we immediately improve all approximation ratios
Sparsification in Algebraic Dynamic Programming
"... Sparsification is a technique to speed up dynamic programming algorithms which has been successfully applied to RNA structure prediction, RNARNAinteraction prediction, simultaneous alignment and folding, and pseudoknot prediction. So far, sparsification has been more a collection of loosely relate ..."
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related examples and no general, well understood theory. In this work we propose a general theory to describe and implement sparsification in dynamic programming algorithms. The approach is formalized as an extension of Algebraic Dynamic Programming (ADP) which makes it applicable to a variety
Spectral Sparsification and Restricted Invertibility
, 2010
"... In this thesis we prove the following two basic statements in linear algebra. Let B be an arbitrary n × m matrix where m ≥ n and suppose 0 < ε < 1 is given. 1. Spectral Sparsification. There is a nonnegative diagonal matrix Sm×m with at most ⌈n/ε2 ⌉ nonzero entries for which (1 − ε) 2BBT ≼ BSB ..."
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Cited by 11 (1 self)
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In this thesis we prove the following two basic statements in linear algebra. Let B be an arbitrary n × m matrix where m ≥ n and suppose 0 < ε < 1 is given. 1. Spectral Sparsification. There is a nonnegative diagonal matrix Sm×m with at most ⌈n/ε2 ⌉ nonzero entries for which (1 − ε) 2BBT
Satisfiability Allows No Nontrivial Sparsification Unless The PolynomialTime Hierarchy Collapses
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 38 (2010)
, 2010
"... Consider the following twoplayer communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computationally unbounded but does not know any part of x; their goal is to cooperatively decide whether x belongs to L at small ..."
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Cited by 53 (2 self)
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areas, namely sparsification, kernelization in parameterized complexity, lossy compression, and probabilistically checkable proofs. By reduction, similar results hold for other NPcomplete problems. For the vertex cover problem on nvertex duniform hypergraphs, the above statement holds for any integer
Sparsification of Rectangular Matrices
, 1996
"... Given a rectangular matrix with more columns than rows, find a base of linear combinations of the row vectors such that these contain as many zero entries as possible. This process is called "sparsification" (of the matrix). A combinatorial search method to solve sparsification is presente ..."
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Cited by 1 (0 self)
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applications of our methods. Keywords Sparsification of matrices, Matroid, Abstract properties of linear dependency, Generalize...
Consistent sparsification for graph optimization
 in Proc. European Conf. Mobile Robotics
, 2013
"... Abstract — In a standard posegraph formulation of simultaneous localization and mapping (SLAM), due to the continuously increasing numbers of nodes (states) and edges (measurements), the graph may grow prohibitively too large for longterm navigation. This motivates us to systematically reduce the ..."
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Cited by 8 (1 self)
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the pose graph amenable to available processing and memory resources. In particular, in this paper we introduce a consistent graph sparsification scheme: i) sparsifying nodes via marginalization of old nodes, while retaining all the information (consistent relative constraints) – which is conveyed
Results 1  10
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