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A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to…
This work analyzes and parallelizes LearnedSort, the novel algorithm that sorts using machine learning models based on the cumulative distribution function. LearnedSort is analyzed under the lens of algorithms with predictions, and it is…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
Suppose $n$ different pairs of socks are put in a tumble dryer. When the dryer is finished socks are taken out one by one, if a sock matches one of the socks on the sorting table both are removed, otherwise it is put on the table until its…
In this work of thesis we introduce and study a new family of sorting devices, which we call pattern-avoiding machines. They consist of two stacks in series, equipped with a greedy procedure. On both stacks we impose a static constraint in…
In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…
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…
Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate…
Given a pattern x of length m and a text y of length n, both over an ordered alphabet, the order-preserving pattern matching problem consists in finding all substrings of the text with the same relative order as the pattern. It is an…
Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology.…
A new Combined Sieve algorithm is presented with cost proportional to the number of enumerated factors over a series of intervals. This algorithm achieves a significant speedup, over a traditional sieve, when handling many ([10^4, 10^7])…
We study the problem of list ranking in the parallel external memory (PEM) model. We observe an interesting dual nature for the hardness of the problem due to limited information exchange among the processors about the structure of the…
We initiate the study of parallel algorithms for fairly allocating indivisible goods among agents with additive preferences. We give fast parallel algorithms for various fundamental problems, such as finding a Pareto Optimal and EF1…
Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…
We introduce a new sorting device for permutations which makes use of a pop stack augmented with a bypass operation. This results in a sorting machine, which is more powerful than the usual Popstacksort algorithm and seems to have never…
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…
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…
Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. Moreover, a cost function is associated with each set. The goal is to…