Variable Min-Cut Max-Flow Bounds and Algorithms in Finite Regime
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909696761266176 |
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| author | Gitik, Rivka Cohen, Alejandro |
| author_facet | Gitik, Rivka Cohen, Alejandro |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variable Min-Cut Max-Flow Bounds and Algorithms in Finite Regime Gitik, Rivka Cohen, Alejandro Information Theory Computational Geometry 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). |
| title | Variable Min-Cut Max-Flow Bounds and Algorithms in Finite Regime |
| topic | Information Theory Computational Geometry |
| url | https://arxiv.org/abs/2507.14852 |