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

TL;DR

This paper introduces a geometric framework to analyze throughput in networks with fluctuating link capacities, deriving new bounds, defining stability, and proposing algorithms to improve network performance and stability.

Contribution

It presents a novel geometric approach to analyze variable-capacity networks, introduces stability notions, and develops efficient algorithms to enforce stability and mitigate delay-throughput tradeoffs.

Findings

Increasing links reduces throughput variability by nearly 90%.

Unstable networks can have exponentially many min-cut sets.

Proposed algorithm enforces stability with quadratic time complexity.

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).