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Approximation Algorithms for the Traveling Thief Problem

Authors Jan Eube , Kelin Luo , Heiko Röglin , Sarah Sturm

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Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Traveling Thief Problem
  • Traveling Salesperson Problem
  • Knapsack Problem
  • Approximation Algorithms
  • Bi-objective optimization

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Abstract

The Traveling Thief Problem (TTP) combines the Traveling Salesperson Problem with the Knapsack Problem. In this problem, a finite metric space is given, and at each location an item with some profit and weight is placed. An agent seeks to collect a subset of the items. To do so, the agent must decide which items to collect and to determine a cyclic tour visiting the corresponding locations. While collecting an item yields its profit as a reward, the agent’s speed decreases as more weight is picked up. The problem involves two competing objectives: maximizing the total profit of the collected items and minimizing the travel time of the tour. 
While many heuristics and exact algorithms (with a non-polynomial running time) have been developed, no approximation algorithms are known for any variant of the TTP. We aim at computing an (α₁,α₂)-approximate Pareto set that, for every solution, contains another solution collecting at least a 1/(α₁) fraction of its profit while requiring at most α₂ times its travel time. Our main result is an algorithm that calculates a (9 + ε,9 + ε)-approximate Pareto set in polynomial time. 
We also consider the setting in which the set of items to be collected is given in advance, so that the agent only has to compute a tour through the corresponding locations that minimizes the total travel time. This is the so-called Weighted TSP. For this setting, we present a (2e + ε)-approximation algorithm.

Cite As Get BibTex

Jan Eube, Kelin Luo, Heiko Röglin, and Sarah Sturm. Approximation Algorithms for the Traveling Thief Problem. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 130:1-130:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.130

Author Details

Jan Eube
  • University of Bonn, Germany
Kelin Luo
  • University at Buffalo, NY, USA
Heiko Röglin
  • University of Bonn, Germany
Sarah Sturm
  • University of Bonn, Germany

Funding

This work has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 390685813; 459420781 and by the Lamarr Institute for Machine Learning and Artificial Intelligence lamarr-institute.org.

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