Related papers: How Good is Multi-Pivot Quicksort?
TimSort is a well-established sorting algorithm whose running time depends on how sorted the input already is. Recently, Eppstein, Goodrich, Illickan, and To designed algorithms inspired by TimSort for Pareto front, planar convex hull, and…
The evaluation of clustering results is difficult, highly dependent on the evaluated data set and the perspective of the beholder. There are many different clustering quality measures, which try to provide a general measure to validate…
In generating large quantities of DNA data, high-throughput sequencing technologies require advanced bioinformatics infrastructures for efficient data analysis. k-mer counting, the process of quantifying the frequency of fixed-length k DNA…
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we formalize the pile shuffle and investigate its capabilities as a sorting device. Our study is novel in that we consider pile shuffle in three…
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…
Recent advancements in pretraining have demonstrated that modern Large Language Models (LLMs) possess the capability to effectively learn arithmetic operations. However, despite acknowledging the significance of digit order in arithmetic…
Shor's algorithm is one of the most significant quantum algorithms. Shor's algorithm can factor large integers with a certain success probability in polynomial time. However, Shor's algorithm requires an unbearable amount of qubits in the…
A hybrid evolutionary algorithm with importance sampling method is proposed for multi-dimensional optimization problems in this paper. In order to make use of the information provided in the search process, a set of visited solutions is…
Operator-splitting methods are widely used to solve differential equations, especially those that arise from multi-scale or multi-physics models, because a monolithic (single-method) approach may be inefficient or even infeasible. The most…
We present a new algorithm for fast record retrieval, distribute-probe-gather, or DPG. DPG has important applications both in sorting and in joins. Current main memory sorting algorithms split their work into three phases: extraction of…
This paper introduces a new comparison base stable sorting algorithm, named RS sort. RS Sort involves only the comparison of pair of elements in an array which ultimately sorts the array and does not involve the comparison of each element…
Variant Stochastic cracking is a significantly more resilient approach to adaptive indexing. It showed [1]that Stochastic cracking uses each query as a hint on how to reorganize data, but not blindly so; it gains resilience and avoids…
A new solution for the Dutch national flag problem is proposed, requiring no three-way comparisons, which gives quicksort a proper worst-case runtime of $O(nk)$ for inputs with $k$ distinct elements. This is used together with other known…
The Bulk-Synchronous Parallel model of computation has been used for the architecture independent design and analysis of parallel algorithms whose performance is expressed not only in terms of problem size n but also in terms of parallel…
Given a sparse matrix $A$, the selected inversion algorithm is an efficient method for computing certain selected elements of $A^{-1}$. These selected elements correspond to all or some nonzero elements of the LU factors of $A$. In many…
Sorting and searching are large parts of database query processing, e.g., in the forms of index creation, index maintenance, and index lookup; and comparing pairs of keys is a substantial part of the effort in sorting and searching. We have…
Database applications are increasingly bottlenecked by memory bandwidth and latency due to the memory wall and the limited scalability of DRAM. Join queries, central to analytical workloads, require intensive memory access and are…
This work presents a novel approach to distribute orbitals into subspaces within electron-pairing-based natural orbital functionals (NOFs). This approach modifies the coupling between weakly and strongly occupied orbitals by applying an…
Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…
The pivot algorithm -- we also call it the pivot chain -- is an algorithm for approximately uniform sampling from $\Omega _{N},$ the set of $N$-step self-avoiding walks on $\mathbb{Z}^{d}$ ($N,$ $d\geq 1$). Based on this algorithm and the…