Related papers: Sorting in One and Two Rounds using $t$-Comparator…
The objective behind the Twin Sort technique is to sort the list of unordered data elements efficiently and to allow efficient and simple arrangement of data elements within the data structure with optimization of comparisons and iterations…
In computer science, sorting algorithms are crucial for data processing and machine learning. Large datasets and high efficiency requirements provide challenges for comparison-based algorithms like Quicksort and Merge sort, which achieve…
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…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…
In the online sorting problem, $n$ items are revealed one by one and have to be placed (immediately and irrevocably) into empty cells of a size-$n$ array. The goal is to minimize the sum of absolute differences between items in consecutive…
We analyze different methods of sorting and selecting a set of objects by their intrinsic value, via pairwise comparisons whose outcome is uncertain. After discussing the limits of repeated Round Robins, two new methods are presented: The…
We consider the problem of sorting $n$ elements subject to persistent random comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability $p$, and comparing the same pair of…
The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
Interest in the random-order model (ROM) leads us to initiate a study of utilizing random-order arrivals to extract random bits with the goal of derandomizing algorithms. Besides producing simple algorithms, simulating random bits through…
Generalized sorting problem, also known as sorting with forbidden comparisons, was first introduced by Huang et al. together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes. We study this problem with additional…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…
Various decision support systems are available that implement Data Mining and Data Warehousing techniques for diving into the sea of data for getting useful patterns of knowledge (pearls). Classification, regression, clustering, and many…
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…
Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic…
Algorithms which sort lists of real numbers into ascending order have been studied for decades. They are typically based on a series of pairwise comparisons and run entirely on chip. However people routinely sort lists which depend on…
Historically, much of machine learning research has focused on the performance of the algorithm alone, but recently more attention has been focused on optimizing joint human-algorithm performance. Here, we analyze a specific type of…
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…