Approximating Temporal Betweenness Centrality through Sampling

Concetti Chiave

The core message of this article is to present MANTRA, a rigorous framework for efficiently approximating the temporal betweenness centrality of nodes and temporal edges in large temporal graphs.

Sintesi

The article introduces MANTRA, a framework for approximating the temporal betweenness centrality in large temporal graphs. The key highlights and insights are:

1. MANTRA extends the state-of-the-art estimator for temporal betweenness centrality to cover different temporal path optimality criteria (shortest, shortest-foremost, prefix-foremost).

2. The article derives new bounds on the sufficient number of samples needed to approximate the temporal betweenness centrality for all nodes. These bounds are governed by three key quantities of the temporal graph: the temporal vertex diameter, average temporal path length, and the maximum variance of the temporal betweenness centrality estimators.

3. The authors propose a novel algorithm to efficiently estimate the key quantities (temporal diameter, average temporal path length, temporal connectivity rate) that the sample complexity bounds depend on. This algorithm uses a mixed approach of sampling and counting, with theoretical guarantees on the approximation quality.

4. The MANTRA framework incorporates the sample complexity bounds and a progressive sampling technique to provide a high-quality approximation of the temporal betweenness centrality. MANTRA improves upon the state-of-the-art ONBRA algorithm in terms of running time, sample size, and required space while maintaining high accuracy.

5. The article provides an extensive experimental evaluation comparing MANTRA with ONBRA on several real-world temporal networks, demonstrating the superior performance of MANTRA.

Statistiche

The temporal graphs used in the experiments have the following key characteristics:

Number of nodes (n) ranging from 1,899 to 1,094,018
Number of temporal edges (|E|) ranging from 59,798 to 6,092,445
Number of unique timestamps (|T|) ranging from 32,823 to 1,105,102
Temporal connectivity rate (ζ) ranging from 0.008 to 0.84
Maximum temporal betweenness centrality (b^(pfm)_max, b^(sh)_max, b^(sfm)_max) ranging from 0.0010 to 0.1383

Citazioni

"MANTRA, a rigorous framework for the approximation of the temporal betweenness of all the vertices and temporal edges in large temporal graphs."
"We derive new bounds on the sufficient number of samples needed to approximate the temporal betweenness centrality for all nodes that are governed by three key quantities of the temporal graph, such as the temporal vertex diameter, average temporal path length, and the maximum variance of the temporal betweenness centrality estimators."
"We propose a novel algorithm to efficiently estimate the key quantities of interests that uses a mixed approach based on sampling and counting."

Approfondimenti chiave tratti da

MANTRA

by Antonio Cruc... alle arxiv.org 04-09-2024

https://arxiv.org/pdf/2304.08356.pdf

Domande più approfondite

How can the MANTRA framework be extended to handle other temporal path optimality criteria beyond the ones considered in this work?

In order to extend the MANTRA framework to handle other temporal path optimality criteria, we can follow a similar approach to the one used in the existing framework. The key steps would involve defining the new optimality criteria for temporal paths, analyzing their computational complexity, and providing polynomial time algorithms to compute the temporal centrality measures based on these criteria.

Definition of New Optimality Criteria: The first step would be to define the new optimality criteria for temporal paths. This involves specifying the characteristics that define an optimal path in the context of the specific application or network analysis task.

Computational Complexity Analysis: Similar to the existing work on temporal betweenness centrality, the computational complexity of the new optimality criteria needs to be analyzed. This will help in understanding the feasibility of computing the centrality measures efficiently.

Algorithm Development: Once the new optimality criteria are defined and their computational complexity is understood, algorithms need to be developed to compute the temporal centrality measures based on these criteria. This may involve adapting existing sampling-based techniques or developing new approaches tailored to the specific criteria.

Experimental Evaluation: It is essential to conduct extensive experimental evaluations to validate the performance of the extended MANTRA framework with the new optimality criteria. This includes comparing the results with exact algorithms and assessing the scalability and efficiency of the framework.

By following these steps, the MANTRA framework can be extended to handle a broader range of temporal path optimality criteria, providing a comprehensive tool for analyzing temporal networks in various domains.

How can the MANTRA framework be extended to handle other temporal path optimality criteria beyond the ones considered in this work?

The MANTRA framework's temporal betweenness centrality approximation has various potential applications beyond network analysis tasks. Some of these applications include:

Social Network Analysis: Temporal betweenness centrality can be used to identify key individuals in evolving social networks. This information can be valuable for targeted marketing, influence analysis, and community detection.

Epidemiology and Disease Spread: Understanding how diseases spread through a population over time is crucial for effective intervention strategies. Temporal betweenness centrality can help identify individuals or locations that play a significant role in the spread of infections.

Traffic and Transportation Planning: Analyzing temporal betweenness centrality in transportation networks can optimize traffic flow, identify critical routes, and improve public transportation systems.

Financial Networks: In financial networks, temporal betweenness centrality can help identify systemic risk factors, monitor market trends, and detect anomalies in transactions over time.

Supply Chain Management: Analyzing temporal betweenness centrality in supply chain networks can optimize logistics, improve inventory management, and enhance overall operational efficiency.

By applying temporal betweenness centrality approximation in these diverse domains, valuable insights can be gained to make informed decisions, optimize processes, and enhance overall system performance.

Can the sampling-based techniques used in MANTRA be adapted to approximate other temporal graph metrics and characteristics beyond betweenness centrality?

Yes, the sampling-based techniques used in MANTRA can be adapted to approximate other temporal graph metrics and characteristics beyond betweenness centrality. By modifying the sampling strategy and the estimation algorithms, the framework can be extended to handle various metrics and characteristics of temporal graphs. Some potential adaptations include:

Temporal Closeness Centrality: Sampling techniques can be used to approximate temporal closeness centrality, which measures how quickly a node can reach all other nodes in a network over time.

Temporal PageRank: Sampling methods can be applied to estimate temporal PageRank, which identifies important nodes in a network based on their connections and influence over time.

Temporal Clustering Coefficient: Sampling algorithms can be tailored to approximate the temporal clustering coefficient, which measures the degree to which nodes in a network tend to cluster together over time.

Temporal Network Resilience: Sampling-based approaches can be used to estimate the resilience of temporal networks to disruptions or failures over time, providing insights into network robustness.

By adapting the sampling techniques and algorithms in MANTRA to handle these and other temporal graph metrics and characteristics, a comprehensive framework can be developed for analyzing and understanding the dynamics of temporal networks in various applications.