Blauth, Jannis, Neuwohner, Meike 
ORCID: 0000-0002-3664-3687, Puhlmann, Luise and Vygen, Jens
(2024)
Improved guarantees for the A Priori TSP.
Mathematics of Operations Research.
ISSN 0364-765X
Abstract
We revisit the a priori TSP (with independent activation) and prove stronger approximation guarantees than were previously known. In the a priori TSP, we are given a metric space (V, c) and an activation probability p(v) for each customer ∈ . We ask for a TSP tour T for V that minimizes the expected length after cutting T short by skipping the inactive customers. All known approximation algorithms select a nonempty subset S of the customers and construct a master route solution, consisting of a TSP tour for S and two edges connecting every customer ∈\ to a nearest customer in S. We address the following questions. If we randomly sample the subset S, what should be the sampling probabilities? How much worse than the optimum can the best master route solution be? The answers to these questions (we provide almost matching lower and upper bounds) lead to improved approximation guarantees: less than 3.1 with randomized sampling and less than 5.9 with a deterministic polynomial-time algorithm.
| Item Type: | Article |
|---|---|
| Additional Information: | © 2024 INFORMS |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 03 Dec 2024 10:24 |
| Last Modified: | 13 Dec 2024 11:45 |
| URI: | http://eprints.lse.ac.uk/id/eprint/126218 |
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