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August 2, 2026Open Access

Deletion-Star Ceilings and a 1.28249 Lower Bound for Cost-Preserving Single-Source Unsplittable Flows

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Randomized approach finds a lower bound for cost-preserving unsplittable flows, indicating new limits in flow theory.

This work aims to establish bounds for cost-preserving single-source unsplittable flows while addressing open conjectures.
Introduced a 17-terminal instance verifying lower bounds through complete enumeration of routings.
Developed upper bounds using a weighted two-permutation prefix system with deletion-star concepts.
Classified theorems by the mechanisms proving them and explored continuum limits.
Established a new lower bound of approximately 1.28249 for cost-preserving flow.
Provided unconditional upper bounds below 2 for specific families of extremal cells.
Verified all numerical findings through exact rational or symbolic arithmetic.

Sergey Nikolenko (2026) studied this question.

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