What question did this study set out to answer?

To explore the limitations of cost preservation in single-source unsplittable flows under specific constraints.

August 1, 2026Open Access

A Planar Lower Bound 1.1397... > 9/8 for Cost-Preserving Single-Source Unsplittable Flows

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Randomized trial discovers a lower bound for cost preservation in unsplittable flows, indicating necessary constants.

To explore the limitations of cost preservation in single-source unsplittable flows under specific constraints.
Constructed a four-terminal planar acyclic family of flows with critical constants evaluated.
Developed a directed spine structure with private exits and specific path configurations.
Verified claims using rational and symbolic arithmetic programs with accessible source code.
Established that every universal constant C in the overload constraint must be at least 1.1397.
Demonstrated that 9/8 is the exact supremum for the three-terminal template related to the counterexample.
Identified structural questions that connect the new findings with broader theoretical limits.

Sergey Nikolenko (2026) studied this question.

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