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The randomized complexity of maintaining the minimum

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Brodal,  Gerth Stølting
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Chaudhuri,  Shiva
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-96-1-014.pdf
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Brodal, G. S., Chaudhuri, S., & Radhakrishnan, J.(1996). The randomized complexity of maintaining the minimum (MPI-I-1996-1-014). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-A18C-7
Abstract
The complexity of maintaining a set under the operations {\sf Insert}, {\sf Delete} and {\sf FindMin} is considered. In the comparison model it is shown that any randomized algorithm with expected amortized cost $t$ comparisons per {\sf Insert} and {\sf Delete} has expected cost at least $n/(e2^{2t})-1$ comparisons for {\sf FindMin}. If {\sf FindMin} 474 is replaced by a weaker operation, {\sf FindAny}, then it is shown that a randomized algorithm with constant expected cost per operation exists, but no deterministic algorithm. Finally, a deterministic algorithm with constant amortized cost per operation for an offline version of the problem is given.