Consensus Algorithms and the Decomposition-Separation Theorem

Wolfowitz’s Theorem and Consensus Algorithms in Hadamard Spaces

We provide a generalization of Wolfowitz’s theorem on the products of stochastic, indecomposable and aperiodic (SIA) matrices to metric spaces with nonpositive curvature. As a result we show convergence for a wide class of distributed consensus algorithms operating on these spaces. AMS Subject Classification (2010): 53C23, 60J20, 65P99.

A decomposition theorem and two algorithms for reticulation-visible networks

In studies of molecular evolution, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For the purpose of validating evolutionary models, biologists check whether or not a phylogenetic tree (resp. cluster) is contained in a phylogenetic net...

New Algorithms for Maximum Weight Matching and a Decomposition Theorem

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A Review on Consensus Algorithms in Blockchain

Block chain technology is a decentralized data storage structure based on a chain of data blocks that are related to each other. Block chain saves new blocks in the ledger without trusting intermediaries through a competitive or voting mechanism. Due to the chain structure or the graph between each block with its previous blocks, it is impossible to change blocking data. Block chain architectur...

Biconjugate Decomposition Using ABS Algorithms