Related papers: K-sort: A new sorting algorithm that beats Heap so…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
Topological sorting is an important technique in numerous practical applications, such as information retrieval, recommender systems, optimization, etc. In this paper, we introduce a problem of generalized topological sorting with…
$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…
The problem of sorting with priced information was introduced by [Charikar, Fagin, Guruswami, Kleinberg, Raghavan, Sahai (CFGKRS), STOC 2000]. In this setting, different comparisons have different (potentially infinite) costs. The goal is…
Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small…
Traditional recommendation systems focus on maximizing user satisfaction by suggesting their favourite items. This user-centric approach may lead to unfair exposure distribution among the providers. On the contrary, a provider-centric…
We present methods for k-means clustering on a stream with a focus on providing fast responses to clustering queries. Compared to the current state-of-the-art, our methods provide substantial improvement in the query time for cluster…
Sparse Subspace Clustering (SSC) has been used extensively for subspace identification tasks due to its theoretical guarantees and relative ease of implementation. However SSC has quadratic computation and memory requirements with respect…
In this paper we consider sorting in the cache-oblivious model of Frigo, Leiserson, Prokop, and Ramachandran (1999). We introduce a new simple sorting algorithm in that model which has asymptotically optimal IO complexity $O(\frac{n}{B}…
This work shows that the following problems are equivalent, both in theory and in practice: - median filtering: given an $n$-element vector, compute the sliding window median with window size $k$, - piecewise sorting: given an $n$-element…
We consider the classical problem of sorting an input array containing $n$ elements, where each element is described with a $k$-bit comparison-key and a $w$-bit payload. A long-standing open problem is whether there exist $(k + w) \cdot o(n…
Priority queues are data structures that maintain a dynamic collection of elements and allow inserting new elements and removing the smallest element. The most widely known and used priority queue is likely the implicit binary heap, even…
QuickSelect (aka Find), introduced by Hoare (1961), is a randomized algorithm for selecting a specified order statistic from an input sequence of $n$ objects, or rather their identifying labels usually known as keys. The keys can be numeric…
The original Leapfrogging Samplesort operates on a sorted sample of size $s$ and an unsorted part of size $s+1$. We generalize this to a sorted sample of size $s$ and an unsorted part of size $(2^k-1)(s+1)$, where $k = O(1)$. We present a…
This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n \lg n - 1.4427n + O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to…
We devise coresets for kernel $k$-Means with a general kernel, and use them to obtain new, more efficient, algorithms. Kernel $k$-Means has superior clustering capability compared to classical $k$-Means, particularly when clusters are…
The $k$-$\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the $k$-means clustering problem where the goal is to cluster a dataset $\mathcal{X} \subset \mathbb{R} ^d$ into $k$ clusters. 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,…
In this paper we investigate the problem of sorting a set of $n$ coins, each with distinct but unknown weights, using an unusual scale. The classical version of this problem, which has been well-studied, gives the user a binary scale,…
This paper presents a family of algorithms for fast subset filtering within ordered sets of integers representing composite keys. Applications include significant acceleration of (ad-hoc) analytic queries against a data warehouse without…