Related papers: QuickMergesort: Practically Efficient Constant-Fac…
Database query processing requires algorithms for duplicate removal, grouping, and aggregation. Three algorithms exist: in-stream aggregation is most efficient by far but requires sorted input; sort-based aggregation relies on external…
Real world datasets are sparse, dirty and contain hundreds of items. In such situations, discovering interesting rules (results) using traditional frequent itemset mining approach by specifying a user defined input support threshold is not…
We provide a probabilistic analysis of the output of Quicksort when comparisons can err.
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
Merging two sorted arrays is a prominent building block for sorting and other functions. Its efficient parallelization requires balancing the load among compute cores, minimizing the extra work brought about by parallelization, and…
We consider online algorithms for the $k$-server problem on trees. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, a naive implementation of their algorithm has…
This paper establishes theoretical bonafides for implicit concurrent multivariate effect evaluation--implicit concurrency for short---a broad and versatile computational learning efficiency thought to underlie general-purpose, non-local,…
An $\varepsilon$-coreset for a given set $D$ of $n$ points, is usually a small weighted set, such that querying the coreset \emph{provably} yields a $(1+\varepsilon)$-factor approximation to the original (full) dataset, for a given family…
In the Equal-Subset-Sum problem, we are given a set $S$ of $n$ integers and the problem is to decide if there exist two disjoint nonempty subsets $A,B \subseteq S$, whose elements sum up to the same value. The problem is NP-complete. The…
We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons,…
We study the Euclidean minimum weight perfect matching problem for $n$ points in the plane. It is known that any deterministic approximation algorithm whose approximation ratio depends only on $n$ requires at least $\Omega(n \log n)$ time.…
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…
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…
Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. The more sophisticated and fast sorting algorithms become asymptotically, the less efficient they are for small sets of items…
It is a long-standing open question to determine the minimum number of comparisons $S(n)$ that suffice to sort an array of $n$ elements. Indeed, before this work $S(n)$ has been known only for $n\leq 22$ with the exception for $n=16$, $17$,…
As generative models scale to larger inputs across language, vision, and video domains, the cost of token-level computation has become a key bottleneck. While prior work suggests that only a subset of tokens significantly influence…
Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$…
We find a succinct expression for computing the sequence $x_t = a_t x_{t-1} + b_t$ in parallel with two prefix sums, given $t = (1, 2, \dots, n)$, $a_t \in \mathbb{R}^n$, $b_t \in \mathbb{R}^n$, and initial value $x_0 \in \mathbb{R}$. On…
We study a fundamental model of online preference aggregation, where an algorithm maintains an ordered list of $n$ elements. An input is a stream of preferred sets $R_1, R_2, \dots, R_t, \dots$. Upon seeing $R_t$ and without knowledge of…
We present sorting algorithms that represent the fastest known techniques for a wide range of input sizes, input distributions, data types, and machines. A part of the speed advantage is due to the feature to work in-place. Previously, the…