Related papers: Quicksort with unreliable comparisons: a probabili…
The linear pivot selection algorithm, known as median-of-medians, makes the worst case complexity of quicksort be $\mathrm{O}(n\ln n)$. Nevertheless, it has often been said that this algorithm is too expensive to use in quicksort. In this…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
We present an average case analysis of a variant of dual-pivot quicksort. We show that the used algorithmic partitioning strategy is optimal, i.e., it minimizes the expected number of key comparisons. For the analysis, we calculate the…
The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort n randomly permuted items is known to be determined implicitly by a distributional fixed-point equation. We give an algorithm for perfect…
The paper questions the robustness of average case time complexity of the fast and popular quicksort algorithm. Among the six standard probability distributions examined in the paper, only continuous uniform, exponential and standard normal…
Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling…
Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite…
When algorithms for sorting and searching are applied to keys that are represented as bit strings, we can quantify the performance of the algorithms not only in terms of the number of key comparisons required by the algorithms but also in…
When the search algorithm QuickSelect compares keys during its execution in order to find a key of target rank, it must operate on the keys' representations or internal structures, which were ignored by the previous studies that quantified…
Machine Translation Quality Estimation is a notoriously difficult task, which lessens its usefulness in real-world translation environments. Such scenarios can be improved if quality predictions are accompanied by a measure of uncertainty.…
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
We revisit the method of Kirschenhofer, Prodinger and Tichy to calculate the moments of comparisons used by the quick sort algorithm. We reemphasize that this approach helps in calculating these quantities with less computation. We also…
We present an average case analysis of two variants of dual-pivot quicksort, one with a non-algorithmic comparison-optimal partitioning strategy, the other with a closely related algorithmic strategy. For both we calculate the expected…
Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.
We provide a smoothed analysis of Hoare's find algorithm and we revisit the smoothed analysis of quicksort. Hoare's find algorithm - often called quickselect - is an easy-to-implement algorithm for finding the k-th smallest element of a…
An industrial grade Quicksort function along with its new algorithm is presented. Compared to 4 other well known implementations of Quicksort, the new algorithm reduces both the number of comparisons and swaps in most cases while staying…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
I prove that the average number of comparisons for median-of-$k$ Quicksort (with fat-pivot a.k.a. three-way partitioning) is asymptotically only a constant $\alpha_k$ times worse than the lower bound for sorting random multisets with…
We consider a simple model of imprecise comparisons: there exists some $\delta>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $\delta$, then the…