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arXiv · 2405.06244

A $(\frac32+\frac1{\mathrm{e}})$-Approximation Algorithm for Ordered TSP

Susanne Armbruster·Matthias Mnich·Martin Nägele
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Abstract

We present a new $(\frac32+\frac1{\mathrm{e}})$-approximation algorithm for the Ordered Traveling Salesperson Problem (Ordered TSP). Ordered TSP is a variant of the classical metric Traveling Salesperson Problem (TSP) where a specified subset of vertices needs to appear on the output Hamiltonian cycle in a given order, and the task is to compute a cheapest such cycle. Our approximation guarantee of approximately $1.868$ holds with respect to the value of a natural new linear programming (LP) relaxation for Ordered TSP. Our result significantly improves upon the previously best known guarantee of $\frac52$ for this problem and thereby considerably reduces the gap between approximability of Ordered TSP and metric TSP. Our algorithm is based on a decomposition of the LP solution into weighted trees that serve as building blocks in our tour construction.

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Susanne Armbruster, Matthias Mnich, Martin Nägele. 2024-05-10. A $(\frac32+\frac1{\mathrm{e}})$-Approximation Algorithm for Ordered TSP. https://arxiv.org/abs/2405.06244

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