Related papers: An Optimal Algorithm for Sorting Pattern-Avoiding …
In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…
Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential…
We propose a supervised learning algorithm for machine learning applications. Contrary to the model developing in the classical methods, which treat training, validation, and test as separate steps, in the presented approach, there is a…
We give optimal sorting algorithms in the evolving data framework, where an algorithm's input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an…
We say a zero-one matrix $A$ avoids another zero-one matrix $P$ if no submatrix of $A$ can be transformed to $P$ by changing some ones to zeros. A fundamental problem is to study the extremal function $ex(n,P)$, the maximum number of…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
Permutation $\sigma$ appears in permutation $\pi$ if there exists a subsequence of $\pi$ that is order-isomorphic to $\sigma$. The natural question is to check if $\sigma$ appears in $\pi$, and if so count the number of occurrences. We know…
With the widespread application of efficient pattern mining algorithms, sequential patterns that allow gap constraints have become a valuable tool to discover knowledge from biological data such as DNA and protein sequences. Among all kinds…
We show that the left-greedy algorithm is a better algorithm than the right-greedy algorithm for sorting permutations using t stacks in series when t>1. We also supply a method for constructing some permutations that can be sorted by t…
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…
Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…
We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking,…
Generalizing stack sorting and $c$-sorting for permutations, we define the permutree sorting algorithm. Given two disjoint subsets $U$ and $D$ of $\{2, \dots, n-1\}$, the $(U,D)$-permutree sorting tries to sort the permutation $\pi \in…
We engineer algorithms for sorting huge data sets on massively parallel machines. The algorithms are based on the multiway merging paradigm. We first outline an algorithm whose I/O requirement is close to a lower bound. Thus, in contrast to…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
A sorting network is a shortest path from 12...n to n...21 in the Cayley graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n->infinity the space-time process of swaps converges to the…
We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian…
In this paper we propose a family of algorithms combining tree-clustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
When iteratively solving linear systems By=b with Hermitian positive semi-definite $B$, and in particular when solving least-squares problems for $Ax=b$ by reformulating them as $AA^\ast y=b$, it is often observed that SOR-type methods…