Concerning nonnegative matrices and doubly stochastic matrices

Sinkhorn, Richard; Knopp, Paul

doi:10.2140/pjm.1967.21.343

Cited by 686 publications

(514 citation statements)

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“…Sinkhorn and Knopp [9] gave another interesting characterization of C A as the limit of an infinite sequence of matrices. Let f , g and h be functions from and to n × n real matrices, defined as follows:…”

Section: Theorem 1 For Any N × N Biadjacency Matrix a Resulting Frommentioning

confidence: 99%

An Accurate System-Wide Anonymity Metric for Probabilistic Attacks

Bagai

et al. 2011

Privacy Enhancing Technologies

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Abstract.We give a critical analysis of the system-wide anonymity metric of Edman et al. [3], which is based on the permanent value of a doubly-stochastic matrix. By providing an intuitive understanding of the permanent of such a matrix, we show that a metric that looks no further than this composite value is at best a rough indicator of anonymity. We identify situations where its inaccuracy is acute, and reveal a better anonymity indicator. Also, by constructing an information-preserving embedding of a smaller class of attacks into the wider class for which this metric was proposed, we show that this metric fails to possess desirable generalization properties. Finally, we present a new anonymity metric that does not exhibit these shortcomings. Our new metric is accurate as well as general.

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Section: Theorem 1 For Any N × N Biadjacency Matrix a Resulting Frommentioning

confidence: 99%

An Accurate System-Wide Anonymity Metric for Probabilistic Attacks

Bagai

et al. 2011

Privacy Enhancing Technologies

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“…In fact, the convergence is very fast in the above process [17]. And because of the rounding loss as we mentioned in section III, the difference between two and twenty iterations is negligible (see the simulation result in the next section).…”

Section: Lemma 41: Let σ Be a Permutation Of {12 …N} And For An Nmentioning

confidence: 86%

“…These two operations are denoted as row and column scaling respectively. In fact, if the initial matrix satisfies some week condition, row and column scaling in an interleaved and iterative way will make the matrix converge to a doubly stochastic matrix [17]:…”

Section: A the Psa Algorithmmentioning

confidence: 99%

Practical Algorithms of Bandwidth Regulation for Rate-Based Switching

Wang¹,

He²,

Zhao³

et al. 2007

IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference

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Abstract-A rate-based switch fabric called smoothed buffer crossbar has been proposed in our recent work. It can provide 100% rate-guaranteed service with only a two-cell buffer at each crosspoint, and can also support best-effort service with an additional bandwidth regulator. However, the widely used maxflow model for bandwidth regulation is neither scalable nor of 100% throughput. In order to evaluate the performance of bandwidth regulator, we first introduce the 100% ideal throughput measurement in this paper. Then we prove that the total arrival average (TAA) algorithm has got this property, which does not happen in the max-flow allocation. Then an O(N) algorithm called proportion scaling allocation (PSA) is presented. Simulations reveal that PSA can deliver nearly 100% throughput even in a frequently changing traffic pattern. As a comparison, both theoretical and experimental evidences are given to show the inefficiency of the max-flow model. Index Terms-switch fabric, rate-based switching, bandwidth regulation, scheduling.

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“…is the vector whose entries are the reciprocal of those of p. A non-trivial result proves that the equation defining power has a solution on a network if and only if the network has a power equilibrium in which the division of the capital on edges is strictly positive [5,1]. Figure 2 depicts the regularizable network of gas pipelines in Europe where node size is proportional to power as computed with the above equation.…”

Section: Application Scenariomentioning

confidence: 99%

“…Observe that the equivalence classes of the relation ↔ are E 1 = {(1, 2), (1, 3), (1, 4), (5, 4), (6, 4)} and E 2 = {(2, 1), (3, 1), (4, 1), (4,5), (4, 6)}. By using two permutation P and Q to move rows 1, 5, 6 (the white nodes of E 1 ) on the top of the matrix and rows 2, 3, 4 (the white nodes of E 2 ) on the bottom and to move columns 2, 3, 4 (the black nodes of E 1 ) on the left and columns 1, 5, 6 (the black nodes of E 2 ) on the right we obtain …”

Section: The Directed Casementioning

confidence: 99%

Arbitrarily regularizable graphs

Franceschet¹,

Bozzo²

2017

Internet Mathematics

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A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative regularizable graphs have been thoroughly investigated in the literature. In this work, we propose and study arbitrarily regularizable graphs. In particular, we investigate necessary and sufficient regularization conditions on the topology of the graph and of the corresponding adjacency matrix. Moreover, we study the computational complexity of the regularization problem and characterize it as a linear programming model.

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Concerning nonnegative matrices and doubly stochastic matrices

Cited by 686 publications

References 3 publications

An Accurate System-Wide Anonymity Metric for Probabilistic Attacks

An Accurate System-Wide Anonymity Metric for Probabilistic Attacks

Practical Algorithms of Bandwidth Regulation for Rate-Based Switching

Arbitrarily regularizable graphs

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