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arXiv · 2610.41178

Traveling Salesman Problem on Graphs with Proportional Independent Set

Ethan X. Fang·Shengtao Guo·Junwei Lu·Yuan Yao
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Abstract

We give a deterministic algorithm for minimum-cost Hamiltonian cycle in undirected graphs with arbitrary real edge costs and an independent set of size at least $αn$, for any fixed $3/7<α\le1/2$. It runs in $O^*(γ(α)^n)$ time for an explicit constant $γ(α)<2$; for bipartite graphs, the bound is $O^*((1+2\sqrt2)^{n/2})\approx O^*(1.957^n)$. The algorithm is based on a restricted Held--Karp dynamic program. Its state enumeration uses structural properties of minimum-cost assignments arising from a regular triangulation of a product of simplices.

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Ethan X. Fang, Shengtao Guo, Junwei Lu, Yuan Yao. 2026-10-30. Traveling Salesman Problem on Graphs with Proportional Independent Set. https://arxiv.org/abs/2610.41178

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