What question did this study set out to answer?

To establish the first unconditional positive bounds and exact-mean decomposition theorems for cost-preserving single-source unsplittable flow problems across diverse network classes.

August 15, 2026Open Access

Exact-Mean Decompositions for Cost-Preserving Single-Source Unsplittable Flows: Demand Scales and Local Interaction Structure

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Authors

SNSergey NikolenkoSt Petersburg University

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Implication

Theoretical analysis establishes exact-mean decompositions for cost-preserving single-source unsplittable flows, proving unconditional positive bounds across multiple network classes.

Key Points

To establish the first unconditional positive bounds and exact-mean decomposition theorems for cost-preserving single-source unsplittable flow problems across diverse network classes.
Characterized optimal cost-preserving additive constants via convex combinations of support routings over arc-deletion closed graph families.
Analyzed local interaction structures using network matrices, total unimodularity, and a tree-path four-coloring theorem.
Verified all numerical results through solver-free analytical proofs certified by dual independent rational arithmetic implementations.
Derived the exact local envelope ladder with E(2) = 1, E(3) = 9/8, and E(4) = (299 - 41*sqrt(41))/32 ≈ 1.13974707 by closing 2,015 boundary cells.
Determined exact constants for specific graph topologies, including 0 for out-trees, 1 for two-layer hubs and outerplanar two-exit spines, and at most 1 for series-parallel networks.
Established a new planar graph lower bound of 58676765987259/50000000000000 ≈ 1.173535 and reduced universal bounds to a certified merger condition with wall K >= 2.565201.

Cite This Study

Sergey Nikolenko (2026) studied this question.

synapsesocial.com/papers/6a801a2875c2e31742c86b95 https://doi.org/10.5281/zenodo.21922203

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Implication

Theoretical analysis establishes exact-mean decompositions for cost-preserving single-source unsplittable flows, proving unconditional positive bounds across multiple network classes.

Exact-Mean Decompositions for Cost-Preserving Single-Source Unsplittable Flows: Demand Scales and Local Interaction Structure

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Member takes

Implication

Key Points

Cite This Study

Exact-Mean Decompositions for Cost-Preserving Single-Source Unsplittable Flows: Demand Scales and Local Interaction Structure

Discussion

Member takes

Implication

Key Points

Cite This Study

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