5,565 research outputs found
Analysis of Algorithms for Permutations Biased by Their Number of Records
The topic of the article is the parametric study of the complexity of
algorithms on arrays of pairwise distinct integers. We introduce a model that
takes into account the non-uniformness of data, which we call the Ewens-like
distribution of parameter for records on permutations: the weight
of a permutation depends on its number of records. We show that
this model is meaningful for the notion of presortedness, while still being
mathematically tractable. Our results describe the expected value of several
classical permutation statistics in this model, and give the expected running
time of three algorithms: the Insertion Sort, and two variants of the Min-Max
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Limiting search cost distribution for the move-to-front rule with random request probabilities
Consider a list of files whose popularities are random. These files are
updated according to the move-to-front rule and we consider the induced Markov
chain at equilibrium. We give the exact limiting distribution of the
search-cost per item as tends to infinity. Some examples are supplied.Comment: move-to-front, search cost, random discrete distribution, limiting
distribution, size biased permutatio
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