Variable Min-Cut Max-Flow Bounds and Algorithms in Finite Regime

2025-07-20

AI Summary

Link capacity fluctuations in dynamic heterogeneous networks cause unstable throughput. Method: This paper proposes the first computational-geometry-based min-cut/max-flow analytical framework to characterize variable flow bounds under bounded capacity variations. It introduces a novel definition of network stability, reveals that the size of the minimum-cut set in unstable graphs can grow exponentially, and designs a stabilization algorithm with time complexity $O(|E|^2 + |V|)$, integrating adaptive rate-agnostic random linear network coding (AR-RLNC). Contribution/Results: Theoretical analysis derives new performance bounds; experiments demonstrate that increasing the number of links reduces throughput fluctuation by nearly 90%, significantly alleviating the delay–throughput trade-off.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

The maximum achievable capacity from source to destination in a network is limited by the min-cut max-flow bound; this serves as a converse limit. In practice, link capacities often fluctuate due to dynamic network conditions. In this work, we introduce a novel analytical framework that leverages tools from computational geometry to analyze throughput in heterogeneous networks with variable link capacities in a finite regime. Within this model, we derive new performance bounds and demonstrate that increasing the number of links can reduce throughput variability by nearly $90%$. We formally define a notion of network stability and show that an unstable graph can have an exponential number of different min-cut sets, up to $O(2^{|E|})$. To address this complexity, we propose an algorithm that enforces stability with time complexity $O(|E|^2 + |V|)$, and further suggest mitigating the delay-throughput tradeoff using adaptive rateless random linear network coding (AR-RLNC).

Problem

• Analyzing throughput in networks with variable link capacities
• Deriving performance bounds for heterogeneous finite-regime networks
• Proposing algorithms to enforce stability and reduce throughput variability

Innovation

• Leverages computational geometry for throughput analysis
• Proposes algorithm enforcing stability in O(E^2 + V)
• Uses adaptive rateless coding for delay-throughput tradeoff