Related papers: The Quicksort algorithm and related topics
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
Motivated by settings such as medical treatments or aircraft maintenance, we consider a scheduling problem with jobs that consist of two operations, a test and a processing part. The time required to execute the test is known in advance…
The classical comparison-based sorting problem asks us to find the underlying total order of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in typical…
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…
In this work, we study the generalized sorting problem, where we are given a set of $n$ elements to be sorted, but only a subset of all possible pairwise element comparisons is allowed. We look at the problem from the perspective of the…
The new dual-pivot Quicksort by Vladimir Yaroslavskiy - used in Oracle's Java runtime library since version 7 - features intriguing asymmetries in its behavior. They were shown to cause a basic variant of this algorithm to use less…
Recent work by Google DeepMind introduced assembly-optimized sorting networks that achieve faster performance for small fixed-size arrays (3-8). In this research, we investigate the integration of these networks as base cases in classical…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained…
Sorting is one of the fundamental problems in computer science. Playing a role in many processes, it has a lower complexity bound imposed by $\mathcal{O}(n\log{n})$ when executing on a sequential machine. This limit can be brought down to…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
We introduce a new algorithm for constructing the generalized suffix array of a collection of highly similar strings. As a first step, we construct a compressed representation of the matching statistics of the collection with respect to a…
We revisit the selection problem, namely that of computing the $i$th order statistic of $n$ given elements, in particular the classic deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973).…
The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire…
The potential harms of algorithmic decisions have ignited algorithmic fairness as a central topic in computer science. One of the fundamental problems in computer science is Set Cover, which has numerous applications with societal impacts,…
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…