Abstract
In this work, we study the advice complexity of the online minimum Steiner tree problem (ST). Given a (known) graph G = (V,E) endowed with a weight function on the edges, a set of N terminals are revealed in a step-wise manner. The algorithm maintains a sub-graph of chosen edges, and at each stage, chooses more edges from G to its solution such that the terminals revealed so far are connected in it. In the standard online setting this problem was studied and a tight bound of O(log(N)) on its competitive ratio is known. Here, we study the power of non-uniform advice and fully characterize it. As a first result we show that using q ·log(|V|) advice bits, where 0 ≤ q ≤ N − 1, it is possible to obtain an algorithm with a competitive ratio of O(log(N/q). We then show a matching lower bound for all values of q, and thus settle the question.
This work was partially supported by SNF grant 200021141089.
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Barhum, K. (2014). Tight Bounds for the Advice Complexity of the Online Minimum Steiner Tree Problem. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds) SOFSEM 2014: Theory and Practice of Computer Science. SOFSEM 2014. Lecture Notes in Computer Science, vol 8327. Springer, Cham. https://doi.org/10.1007/978-3-319-04298-5_8
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DOI: https://doi.org/10.1007/978-3-319-04298-5_8
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