Improved Approximation Ratio for Strategyproof Facility Location on a Cycle
Abstract
We study the problem of design of strategy-proof in expectation (SP) mechanisms for facility location on a cycle, with the objective of minimizing the sum of costs of n agents. We show that there exists an SP mechanism that attains an approximation ratio of 7/4 with respect to the sum of costs of the agents, thus improving the best known upper bound of 2 - 2/n in the cases of n ≥ 5. The mechanism obtaining the bound randomizes between two mechanisms known in the literature: the Random Dictator (RD) and the Proportional Circle Distance (PCD) mechanism of Meir (2019). To prove the result, we propose a cycle-cutting technique that allows for estimating the problem on a cycle by a problem on a line.
Cite
Text
Rogowski and Dziubinski. "Improved Approximation Ratio for Strategyproof Facility Location on a Cycle." International Joint Conference on Artificial Intelligence, 2025. doi:10.24963/IJCAI.2025/449Markdown
[Rogowski and Dziubinski. "Improved Approximation Ratio for Strategyproof Facility Location on a Cycle." International Joint Conference on Artificial Intelligence, 2025.](https://mlanthology.org/ijcai/2025/rogowski2025ijcai-improved/) doi:10.24963/IJCAI.2025/449BibTeX
@inproceedings{rogowski2025ijcai-improved,
title = {{Improved Approximation Ratio for Strategyproof Facility Location on a Cycle}},
author = {Rogowski, Krzysztof and Dziubinski, Marcin},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2025},
pages = {4032-4039},
doi = {10.24963/IJCAI.2025/449},
url = {https://mlanthology.org/ijcai/2025/rogowski2025ijcai-improved/}
}