Streaming Tour Construction from Held–Karp Estimation

Construct graph-metric TSP tours, rather than only estimating their costs, using a streaming method based on the Held–Karp estimation framework.

Background

The algorithm estimates the Held–Karp value and transfers that estimate into approximation guarantees for the graph-metric TSP cost, but it does not output a tour. The paper explicitly identifies tour construction as an unresolved direction for the presented method.

References

Tour construction and a distance-query version remain open for this method.

— Semi-Streaming Estimation of the Held--Karp Bound and Graph-Metric TSP Cost  (2610.18705 - Alipour, 13 Oct 2026) in Section 5, “Limitations and open questions” (Section \ref{sec:limits})