Geodesic
On the Advice Complexity of Online Matching on the Line
Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 3.

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We consider the 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, for each $0 we present a $c(n/k)$-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. 
@article{DMTCS_2024_26_3_a17,
     author = {Csaba, B\'ela and Nagy-Gy\"orgy, Judit},
     title = {On the {Advice} {Complexity} of {Online} {Matching} on the {Line}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2024},
     doi = {10.46298/dmtcs.14125},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.14125/}
}
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Csaba, Béla; Nagy-György, Judit. On the Advice Complexity of Online Matching on the Line. Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 3. doi : 10.46298/dmtcs.14125. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.14125/

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