English
Related papers

Related papers: Online validation of the pi and pi' failure functi…

200 papers

A border u of a word w is a proper factor of w occurring both as a prefix and as a suffix. The maximal unbordered factor of w is the longest factor of w which does not have a border. Here an O(n log n)-time with high probability (or O(n log…

Data Structures and Algorithms · Computer Science 2018-07-03 Tomasz Kociumaka , Ritu Kundu , Manal Mohamed , Solon P. Pissis

While obtaining optimal algorithms for the most important problems in the LOCAL model has been one of the central goals in the area of distributed algorithms since its infancy, tight complexity bounds are elusive for many problems even when…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-06 Sebastian Brandt , Ananth Narayanan

Integer linear programs $\min\{c^T x : A x = b, x \in \mathbb{Z}^n_{\ge 0}\}$, where $A \in \mathbb{Z}^{m \times n}$, $b \in \mathbb{Z}^m$, and $c \in \mathbb{Z}^n$, can be solved in pseudopolynomial time for any fixed number of constraints…

Data Structures and Algorithms · Computer Science 2024-09-06 Lars Rohwedder , Karol Węgrzycki

This paper describes recent advances in the combinatorial method for computing $\pi(x)$, the number of primes $\leq x$. In particular, the memory usage has been reduced by a factor of $\log x$, and modifications for shared- and…

Number Theory · Mathematics 2015-06-01 Douglas B. Staple

We present an algorithm running in time O(n ln n) which decides if a wreath-closed permutation class Av(B) given by its finite basis B contains a finite number of simple permutations. The method we use is based on an article of Brignall,…

Data Structures and Algorithms · Computer Science 2011-03-30 Frédérique Bassino , Mathilde Bouvel , Adeline Pierrot , Dominique Rossin

Given a pattern $w$ and a text $t$, the speed of a pattern matching algorithm over $t$ with regard to $w$, is the ratio of the length of $t$ to the number of text accesses performed to search $w$ into $t$. We first propose a general method…

Data Structures and Algorithms · Computer Science 2016-11-29 Gilles Didier , Laurent Tichit

The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…

Information Theory · Computer Science 2024-02-05 Jens Zumbrägel

In the online labeling problem with parameters n and m we are presented with a sequence of n keys from a totally ordered universe U and must assign each arriving key a label from the label set {1,2,...,m} so that the order of labels…

Data Structures and Algorithms · Computer Science 2012-10-12 Martin Babka , Jan Bulánek , Vladimír Čunát , Michal Koucký , Michael Saks

The Work Function Algorithm is the most effective deterministic on-line algorithm for the k-server problem. Koutsoupias and Papadimitriou proved WFA is (2k-1) competitive. However the best known implementation of WFA requires time O(i^2) to…

Data Structures and Algorithms · Computer Science 2012-03-23 Livio Colussi

The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class,…

Data Structures and Algorithms · Computer Science 2016-05-26 Joan Boyar , Lene M. Favrholdt , Christian Kudahl , Jesper W. Mikkelsen

Many AI-related reasoning problems are based on the problem of satisfiability of propositional formulas with some cardinality-minimality condition. While the complexity of the satisfiability problem (SAT) is well understood when considering…

Computational Complexity · Computer Science 2023-03-06 Nadia Creignou , Frédéric Olive , Johannes Schmidt

We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under letter substitutions on w. We…

Formal Languages and Automata Theory · Computer Science 2021-06-07 Antoine Amarilli , Louis Jachiet , Charles Paperman

We consider the {\it indexable dictionary} problem, which consists of storing a set $S \subseteq \{0,...,m-1\}$ for some integer $m$, while supporting the operations of $\Rank(x)$, which returns the number of elements in $S$ that are less…

Data Structures and Algorithms · Computer Science 2011-08-10 Rajeev Raman , Venkatesh Raman , Srinivasa Rao Satti

Online linear programming (OLP) has found broad applications in revenue management and resource allocation. State-of-the-art OLP algorithms achieve low regret by repeatedly solving linear programming (LP) subproblems that incorporate…

Machine Learning · Statistics 2025-11-04 Jingruo Sun , Wenzhi Gao , Ellen Vitercik , Yinyu Ye

The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. For any given…

Dynamical Systems · Mathematics 2018-03-01 C. Mauduit , C. -G. Moreira

The POPLMARK Challenge comprises a set of problems intended to measure the strength of reasoning systems in the realm of mechanizing programming language meta-theory at the time the challenge was enunciated. Included in the collection is…

Logic in Computer Science · Computer Science 2021-12-20 Gopalan Nadathur

We show that the absolute worst case time complexity for Hopcroft's minimization algorithm applied to unary languages is reached only for de Bruijn words. A previous paper by Berstel and Carton gave the example of de Bruijn words as a…

Data Structures and Algorithms · Computer Science 2007-05-23 Andrei Paun

We study various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to…

Data Structures and Algorithms · Computer Science 2016-08-01 Thomas Kesselheim , Andreas Tönnis

We provide a new online learning algorithm which utilizes online passive-aggressive learning (PA) and total-error-rate minimization (TER) for binary classification. The PA learning establishes not only large margin training but also the…

Machine Learning · Statistics 2020-02-06 Se-In Jang

Two permutations $(x_1,\dots,x_w)$ and $(y_1,\dots,y_w)$ are weakly similar if $x_i<x_{i+1}$ if and only if $y_i<y_{i+1}$ for all $1\leqslant i \leqslant w$. Let $\pi$ be a permutation of the set $[n]=\{1,2,\dots, n\}$ and let $wt(\pi)$…

Combinatorics · Mathematics 2020-12-22 Andrzej Dudek , Jarosław Grytczuk , Andrzej Ruciński