Programming models and runtimes

Costa, Georges Da; Lastovetsky, Alexey; Barbosa, Jorge G.; Díaz‐Martín, Juan C.; Zapata, J.; Janetschek, Matthias; Jeannot, Emmanuel; Leitão, João; Manumachu, Ravi Reddy; Prodan, Radu; Rico‐Gallego, Juan‐Antonio; Roy, Peter Van; Shoker, Ali; Linde, Albert van der

doi:10.1049/pbpc024e_ch2

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2021

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“…This is significant because it allows us to overcome a technical difficulty of the cited work, obtaining error bounds (Theorem 4) as a function of the potential, not of the weights. A case of application of this method of weights from a potential is our contribution (Chapter 2.4) to the collective work [8]. In that work, we used the Laplacian matrix with potentials to perform spectral graph partitioning for process placement on heterogeneous computing platforms.…”

Section: Introductionmentioning

confidence: 99%

Clustering Vertex-Weighted Graphs by Spectral Methods

Zapata

Grácio

2021

Mathematics

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Spectral techniques are often used to partition the set of vertices of a graph, or to form clusters. They are based on the Laplacian matrix. These techniques allow easily to integrate weights on the edges. In this work, we introduce a p-Laplacian, or a generalized Laplacian matrix with potential, which also allows us to take into account weights on the vertices. These vertex weights are independent of the edge weights. In this way, we can cluster with the importance of vertices, assigning more weight to some vertices than to others, not considering only the number of vertices. We also provide some bounds, similar to those of Chegeer, for the value of the minimal cut cost with weights at the vertices, as a function of the first non-zero eigenvalue of the p-Laplacian (an analog of the Fiedler eigenvalue).

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Section: Introductionmentioning

confidence: 99%