Abstract
In this paper the well-known problem of finding the median of an ordered set is studied under a very restrictive streaming model with sequential read-only access to the data. Only a constant number of reference objects from the stream can be stored for comparison with subsequent stream elements. A first non-trivial bound of \(\Omega(\sqrt{n})\) distance to the extrema of the set is presented for a single pass over streams which do not reveal their total size n. For cases with known size, an algorithm is given which guarantees a distance of Ω(n 1 − ε) to the extrema, which is an ε-approximation for the proven best bound possible.
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Lenz, T. (2006). Deterministic Splitter Finding in a Stream with Constant Storage and Guarantees. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_5
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DOI: https://doi.org/10.1007/11940128_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49694-6
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