Abstract
The complexity of maintaining a set under the operations Insert, Delete and FindMin is considered. In the comparison model it is shown that any randomized algorithm with expected amortized cost t comparisons per Insert and Delete has expected cost at least n/(e22t) − 1 comparisons for FindMin. If FindMin is replaced by a weaker operation, 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.
Supported by the Danish Natural Science Research Council (Grant No. 9400044). This research was done while visiting the Max-Planck Institut für Informatik, Saabrücken, Germany.
This work was partially supported by the EU ESPRIT LTR project No. 20244 (ALCOM IT).
Basic Research in Computer Science, a Centre of the Danish National Research Foundation.
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Brodal, G.S., Chaudhuri, S., Radhakrishnan, J. (1996). The randomized complexity of maintaining the minimum. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_116
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DOI: https://doi.org/10.1007/3-540-61422-2_116
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