Cycle analysis of Directed Acyclic Graphs

Vasiliauskaite, Vaiva; Evans, T. S.; Expert, Paul

doi:10.1016/j.physa.2022.127097

Cited by 4 publications

(4 citation statements)

References 30 publications

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“…Our work could also be integrated with existing literature on higher-order motifs in hypergraphs [39,40]. Further research could also be done on analyzing the DAG structures we investigated here using recent work on the cyclic analysis of DAGs [61].…”

Section: Discussionmentioning

confidence: 99%

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Encapsulation structure and dynamics in hypergraphs

LaRock,

Lambiotte

2023

J. Phys. Complex.

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Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world hypergraphs, focusing on the encapsulation of their hyperedges, which is the extent that smaller hyperedges are subsets of larger hyperedges. Building on the concept of line graphs, our measures quantify the relations existing between hyperedges of different sizes and, as a byproduct, the compatibility of the data with a simplicial complex representation -- whose encapsulation would be maximum. We then turn to the impact of the observed structural patterns on diffusive dynamics, focusing on a variant of threshold models, called encapsulation dynamics, and demonstrate that non-random patterns can accelerate the spreading in the system.

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Section: Discussionmentioning

confidence: 99%

“…Here we analyze the height of rooted paths in the transitively reduced DAG, inspired by the approach taken in [61]. A rooted path is one that begins from a root node, which we define as a node in the DAG with zero in-degree and non-zero out-degree.…”

Section: Paths Through Encapsulation Dagsmentioning

confidence: 99%

Encapsulation structure and dynamics in hypergraphs

LaRock,

Lambiotte

2023

J. Phys. Complex.

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“…Mathematically, this can be described using a graph where vertices represent blocks and edges represent links from a block to its "parents". For the i-th block, write the relationship with its parent blocks p and q, where p is the block chosen at random, and q is the last block processed by the same node: (3) where B i denotes the new block, and B p and B q denote the parent blocks. The adjacency matrix A for a graph with n blocks would look like this: -if the j-th block is one of the parents of the i-th block (i.e., if j = p or j = q for block i ).…”

Section: Methods Of Researchmentioning

confidence: 99%

“…The complexity arises from two facets: firstly, the intricate order relationships inherent in the DAG structure, and secondly, the presence of "missing information, " signifying relationships in the partially ordered set (poset) that do not manifest as explicit edges within the DAG. This article delves into characterizing the mesoscopic structures within DAGs, shedding light on the intricate interplay between observed and unobserved transitive edges within the underlying poset [3].…”

Section: Introductionmentioning

confidence: 99%

Development of Dag Blockchain Model

Tokhmetov,

Lee,

Tanchenko

2024

sjaitu

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In this study the authors present an innovative approach to resolving scalability and efficiency challenges in blockchain technology through the integration of Directed Acyclic Graphs (DAGs). This approach helps to overcome the limitations of traditional blockchain systems, particularly in transaction processing. The classic blockchain has some problems as slow transaction processing and poor scalability. The authors offer Directed Acyclic Graph (DAG) as a scalable and energy-efficient alternative. The paper outlines the development of a DAG-based blockchain model, utilizing Python and Flask alongside the Ed25519 cryptographic curve. It conducts a comparative analysis of DAG with traditional consensus mechanisms like Proof of Work and Proof of Stake, underscoring the efficiency and security benefits of employment of DAG. The research methodology includes an extensive literature review and the construction of a practical model to demonstrate DAG's applicability in blockchain networks. Particularly notable is the exploration of DAG's potential in Internet of Things (IoT) ecosystems, addressing critical issues such as energy inefficiency and network communication challenges in existing consensus algorithms. The authors calculated the performance of the model and compared it with similar models on several evaluation criteria. The simulation results of our proposed model show an improvement in performance and security by minimizing end-to-end delay, time cost, energy consumption, and throughput. The model eliminates the limitations of classic blockchain systems, such as high latency and low scalability. It structures transactions and blocks as a DAG, which provides fast validation and high scalability without compromising security. The research demonstrates the transformative implications of DAG for advancing blockchain technology.

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APapo: An asynchronous parallel optimization method for DNN models

Liu,

2024

Future Generation Computer Systems

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Cycle analysis of Directed Acyclic Graphs

Cited by 4 publications

References 30 publications

Encapsulation structure and dynamics in hypergraphs

Encapsulation structure and dynamics in hypergraphs

Development of Dag Blockchain Model

APapo: An asynchronous parallel optimization method for DNN models

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