On the Advice Complexity of Online Matching on the Line
<|reference_start|>On the Advice Complexity of Online Matching on the Line: We consider the weighted matching problem on the line with advice complexity. We give a 1-competitive online algorithm with advice complexity $n-1,$ and show that there is no 1-competitive online algorithm reading less than $n-1$ bits of advice. Moreover, we present a weakly $c(n/k)$-competitive online algorithm with advice complexity $O(k(\log N + \log n))$ where $n$ is the number of servers, $N$ is the distance of the minimal and maximal servers, and $c(n)$ is the complexity of the best online algorithm without advice.<|reference_end|>
@article{csaba2024on,
    title={On the Advice Complexity of Online Matching on the Line},
    author={B'ela Csaba, Judit Nagy-Gy"orgy},
    journal={arXiv preprint arXiv:2408.11161},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11161},
    primaryClass={cs.DS}
}