Related papers: Analysis of the expected number of bit comparisons…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
We show that several versions of Floyd and Rivest's algorithm Select [Comm.\ ACM {\bf 18} (1975) 173] for finding the $k$th smallest of $n$ elements require at most $n+\min\{k,n-k\}+o(n)$ comparisons on average, even when equal elements…
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…
Rank and select are fundamental operations in succinct data structures, that is, data structures whose space consumption approaches the information-theoretic optimal. The performance of these primitives is central to the overall performance…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…
While existing social networking services tend to connect people who know each other, people show a desire to also connect to yet unknown people in physical proximity. Existing research shows that people tend to connect to similar people.…
This paper shows an application of the theory of sorting networks to facilitate the synthesis of optimized general purpose sorting libraries. Standard sorting libraries are often based on combinations of the classic Quicksort algorithm with…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
We provide a probabilistic analysis of the output of Quicksort when comparisons can err.
Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations (AND,OR,NOT) that are ideally suited for…
In this master thesis we analyze the complexity of sorting a set of strings. It was shown that the complexity of sorting strings can be naturally expressed in terms of the prefix trie induced by the set of strings. The model of computation…
We present numerical results for the probability of bad cases for Quicksort, i.e. cases of input data for which the sorting cost considerably exceeds that of the average. Dynamic programming was used to compute solutions of the recurrence…
In this paper, we introduce a family of sequential decision-making problems, collectively termed the Keychain Problem, that involve exploring a set of actions to maximize expected payoff when only a subset of actions are available in each…
We consider the \emph{approximate minimum selection} problem in presence of \emph{independent random comparison faults}. This problem asks to select one of the smallest $k$ elements in a linearly-ordered collection of $n$ elements by only…
This article describes an efficient procedure for computing approximate confidence levels for searches for new particles where the expected signal and background levels are small enough to require the use of Poisson statistics. The results…
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can…
Bitmap indexes are routinely used to speed up simple aggregate queries in databases. Set operations such as intersections, unions and complements can be represented as logical operations (AND, OR, NOT). However, less is known about the…
Semisort is a fundamental algorithmic primitive widely used in the design and analysis of efficient parallel algorithms. It takes input as an array of records and a function extracting a \emph{key} per record, and reorders them so that…
In many data analysis pipelines, a basic and time-consuming process is to produce join results and feed them into downstream tasks. Numerous enumeration algorithms have been developed for this purpose. To be a statistically meaningful…