We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to changes in the cost function. Various algorithms have been shown to give a 2-approximation to the MinSum allocation problem. By analysing such an auction algorithm, we obtain intervals on each cost, such that any fluctuation of the costs within these intervals will result in the auction algorithm outputting the same solution.
@article{arxiv.2306.16032,
title = {Auction algorithm sensitivity for multi-robot task allocation},
author = {Katie Clinch and Tony A. Wood and Chris Manzie},
journal= {arXiv preprint arXiv:2306.16032},
year = {2023}
}