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

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.06244
 arXiv:
 arXiv:2405.06244
 Bibcode:
 2024arXiv240506244A
 Keywords:

 Computer Science  Data Structures and Algorithms