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15,356
Spectral Sparsification and Spectrally Thin Trees
, 2012
"... We provide results of intensive experimental data in order to investigate the existence of spectrally thin trees and unweighted spectral sparsifiers for graphs with small expansion. In addition, we also survey and prove some partial results on the existence of spectrally thin trees on dense graphs w ..."
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We provide results of intensive experimental data in order to investigate the existence of spectrally thin trees and unweighted spectral sparsifiers for graphs with small expansion. In addition, we also survey and prove some partial results on the existence of spectrally thin trees on dense graphs
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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of expanders, which are constantdegree approximations of the complete graph. Our quantitative bounds are within a factor of two of those achieved by the celebrated Ramanujan graphs. We then present a second graph sparsification algorithm based on random sampling, which produces weaker sparsifiers with O(n log
Random Projections, Graph Sparsification, and Differential Privacy
"... Abstract. This paper initiates the study of preserving differential privacy (DP) when the dataset is sparse. We study the problem of constructing efficient sanitizer that preserves DP and guarantees high utility for answering cutqueries on graphs. The main motivation for studying sparse graphs ari ..."
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Cited by 3 (2 self)
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Abstract. This paper initiates the study of preserving differential privacy (DP) when the dataset is sparse. We study the problem of constructing efficient sanitizer that preserves DP and guarantees high utility for answering cutqueries on graphs. The main motivation for studying sparse graphs
Chapter 1 Sampling and Counting
"... The classical Monte Carlo method is an approach to estimating quantities that are hard to compute exactly. The quantity z of interest is expressed as the expectation z = E(Z) of a random variable (r.v.) Z over a probability space Ω,µ. It is assumed that some efficient procedure for sampling from Ω,µ ..."
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The classical Monte Carlo method is an approach to estimating quantities that are hard to compute exactly. The quantity z of interest is expressed as the expectation z = E(Z) of a random variable (r.v.) Z over a probability space Ω,µ. It is assumed that some efficient procedure for sampling from Ω
Faster subset selection for matrices and applications
 SIAM J. Matrix Anal. Appl
"... Abstract. We study the following problem of subset selection for matrices: given a matrix X ∈ Rn×m (m> n) and a sampling parameter k (n ≤ k ≤ m), select a subset of k columns from X such that the pseudoinverse of the sampled matrix has as small a norm as possible. In this work, we focus on the Fr ..."
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Cited by 4 (2 self)
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Abstract. We study the following problem of subset selection for matrices: given a matrix X ∈ Rn×m (m> n) and a sampling parameter k (n ≤ k ≤ m), select a subset of k columns from X such that the pseudoinverse of the sampled matrix has as small a norm as possible. In this work, we focus
Computing A DiameterConstrained Minimum Spanning Tree
, 2001
"... In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path wi ..."
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Cited by 10 (0 self)
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In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path
Complexity Analysis of Tries and Spanning Tree Problems
, 2009
"... Much of the research progress that is achieved nowadays in various scientific fields has its origin in the increasing computational power and the elaborated mathematical theory which are available for processing data. For example, efficient algorithms and data structures play an important role in ..."
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in modern biology: the research field that has only recently grown out of biology and informatics is called bioinformatics. String and prefix matching operations on DNA or protein sequences are among the most important kinds of operations in contemporary bioinformatics applications. The importance of those
Results 1  10
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15,356