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The Randomized Complexity of Maintaining the Minimum
, 1996
"... . 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=(e2 2t ) \Gamma 1 comparisons for Fi ..."
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Cited by 7 (5 self)
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. 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=(e2 2t ) \Gamma 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; in contrast, it is shown that no deterministic algorithm can have constant cost per operation. Finally, a deterministic algorithm with constant amortized cost per operation for an offline version of the problem is given. CR Classification: F.2.2 1. Introduction We consider the complexity of maintaining a set S of elements from a totally ordered universe under the following operations: Insert(x): inserts the element x into S, Delete(x): removes from S the element x provided it is known where x is stored, and Supported by the Danish...
AverageCase Analysis of GraphSearching Algorithms
, 1990
"... Sarantos Kapidakis Advisor  Professor Robert Sedgewick We estimate the expected value of various search quantities for a variety of graphsearching methods, for example depthfirst search and breadthfirst search. Our analysis applies to both directed and undirected random graphs, and it covers th ..."
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Cited by 2 (0 self)
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Sarantos Kapidakis Advisor  Professor Robert Sedgewick We estimate the expected value of various search quantities for a variety of graphsearching methods, for example depthfirst search and breadthfirst search. Our analysis applies to both directed and undirected random graphs, and it covers the range of interesting graph densities, including densities at which a random graph is disconnected with a giant connected component. We estimate the number of edges examined during the search, since this number is proportional to the running time of the algorithm. We find that for hardly connected graphs, all of the edges might be examined, but for denser graphs many fewer edges are generally required. We prove that any searching algorithm examines \Theta(n log n) edges, if present, on all random graphs with n nodes but not necessarily on the complete graphs. One property of some searching algorithms is the maximum depth of the search. In depthfirst search, this depth can be used to estima...