Abstract
We study the Online Steiner Tree Leasing (OSTL) problem, defined in a weighted undirected graph with a distinguished root node r. There is a known set \(\mathcal {L}\) of available lease types, where each type \(\ell \in \mathcal {L}\) is characterized by its duration \(D_\ell \) and cost factor \(C_\ell \). As an input, an online algorithm is given a sequence of terminals and has to connect them to the root r using leased edges. An edge of length d can be leased using lease type \(\ell \) for cost \(C_\ell \cdot d\) and remains valid for time \(D_\ell \).
The OSTL problem contains the online Steiner tree and the single-source rent-or-buy problems as specific subcases. We present the first deterministic online algorithm for OSTL, whose competitive ratio is \(O(|\mathcal {L}| \cdot \log k)\), where k is the number of different terminals in the input. The currently best randomized algorithm attains the ratio of \(O(\log |\mathcal {L}| \cdot \log n)\), where \(n \ge k\) is the number of nodes in the graph.
Partially supported by the Polish National Science Centre grant 2016/22/E/ST6/00499.
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Bienkowski, M., Kraska, A., Schmidt, P. (2017). A Deterministic Algorithm for Online Steiner Tree Leasing. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_15
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