Abstract
We give a worst-case Ω(n 2/log n )lower bound on the number of vertex evaluations a deterministic algorithm needs to perform in order to find the (unique)sink of a unique sink oriented n-dimensional cube. We consider the problem in the vertex-oracle model, introduced in [17]. In this model one can access the orientation implicitly, in each vertex evaluation an oracle discloses the orientation of the edges incident to the queried vertex.An important feature of the model is that the access is indeed arbitrary, the algorithm does not have to proceed on a directed path in a simplex-like fashion, but could “jump around”.Our result is the first super-linear lower bound on the problem. The strategy we describe works even for acyclic orientations.We also give improved lower bounds for small values of n and fast algorithms in a couple of important special classes of orientations to demonstrate the difficulty of the lower bound problem.
Supported by the joint Berlin/Zürich graduate program Combinatorics, Geometry, and Computation (CGC), financed by German Science Foundation (DFG)and ETH Zurich.
Supported by the joint Berlin/Zürich graduate program Combinatorics, Geometry, and Computation (CGC),financed by German Science Foundation (DFG)and ETH Zurich,and by NSF grant DMS 99-70270.
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Schurr, I., Szabó, T. (2002). Finding the Sink Takes Some Time. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_72
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DOI: https://doi.org/10.1007/3-540-45749-6_72
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