eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-09-16
1:1
1:18
10.4230/LIPIcs.APPROX/RANDOM.2024.1
article
A (3/2 + 1/e)-Approximation Algorithm for Ordered TSP
Armbruster, Susanne
1
https://orcid.org/0009-0003-0597-033X
Mnich, Matthias
2
https://orcid.org/0000-0002-4721-5354
Nägele, Martin
3
https://orcid.org/0000-0002-3059-6402
Research Institute for Discrete Mathematics and Hausdorff Center for Mathematics, University of Bonn, Germany
Hamburg University of Technology, Institute for Algorithms and Complexity, Hamburg, Germany
Department of Mathematics, ETH Zurich, Zurich, Switzerland
We present a new (3/2 + 1/e)-approximation algorithm for the Ordered Traveling Salesperson Problem (Ordered TSP). Ordered TSP is a variant of the classic 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 5/2 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol317-approx-random2024/LIPIcs.APPROX-RANDOM.2024.1/LIPIcs.APPROX-RANDOM.2024.1.pdf
Travelling Salesperson Problem
precedence constraints
linear programming
approximation algorithms