Search results for " Data Structures"
showing 10 items of 80 documents
Improving table compression with combinatorial optimization
2002
We study the problem of compressing massive tables within the partition-training paradigm introduced by Buchsbaum et al. [SODA'00], in which a table is partitioned by an off-line training procedure into disjoint intervals of columns, each of which is compressed separately by a standard, on-line compressor like gzip. We provide a new theory that unifies previous experimental observations on partitioning and heuristic observations on column permutation, all of which are used to improve compression rates. Based on the theory, we devise the first on-line training algorithms for table compression, which can be applied to individual files, not just continuously operating sources; and also a new, …
Some complexity and approximation results for coupled-tasks scheduling problem according to topology
2016
International audience; We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain,. . .). In such a context, we design some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters.
Algorithms for Computing Abelian Periods of Words
2012
Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the notion of an \emph{Abelian period} of a word. A word of length $n$ over an alphabet of size $\sigma$ can have $\Theta(n^{2})$ distinct Abelian periods. The Brute-Force algorithm computes all the Abelian periods of a word in time $O(n^2 \times \sigma)$ using $O(n \times \sigma)$ space. We present an off-line algorithm based on a $\sel$ function having the same worst-case theoretical complexity as the Brute-Force one, but outperforming it in practice. We then present on-line algorithms that also enable to compute all the Abelian periods of all the prefixes of $w$.
On Combinatorial Generation of Prefix Normal Words
2014
A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present an efficient algorithm for exhaustively listing the prefix normal words with a fixed length. The algorithm is based on the fact that the language of prefix normal words is a bubble language, a class of binary languages with the property that, for any word w in the language, exchanging the first occurrence of 01 by 10 in w results in another word in the language. We prove that each prefix normal word is produced in O(n) amortized time, and conjecture, based on expe…
Pattern detection in ordered graphs
2023
A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In contrast, many essential graph classes can be recognized efficiently thanks to characterizations of the following form: there must exist an ordering of the vertices such that some ordered pattern does not appear, where a pattern is basically an ordered subgraph. These pattern characterizations have been studied for decades, but there have been recent efforts to better understand them systematically. In this paper, we focus on a simple problem at the core of th…
Algorithms for Anti-Powers in Strings
2018
Abstract A string S [ 1 , n ] is a power (or tandem repeat) of order k and period n / k if it can be decomposed into k consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient computation have wide application and are heavily studied. Recently, Fici et al. (Proc. ICALP 2016) defined an anti-power of order k to be a string composed of k pairwise-distinct blocks of the same length ( n / k , called anti-period). Anti-powers are a natural converse to powers, and are objects of combinatorial interest in their own right. In this paper we initiate the algorithmic study of anti-powers. Given a string S, we describe an op…
Normal, Abby Normal, Prefix Normal
2014
A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number $pnw(n)$ of prefix normal words of length $n$, showing that $pnw(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)$ for some $c$ and $pnw(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)$. We introduce efficient algorithms for testing the prefix normal property and a "mechanical algorithm" for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes to stay normal but Bob wants t…
A note on easy and efficient computation of full abelian periods of a word
2016
Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.
A subquadratic algorithm for minimum palindromic factorization
2014
We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns the minimum number of palindromes $S_1,\ldots, S_\ell$ such that $S = S_1 \cdots S_\ell$. We also show that the time complexity is $\mathcal{O}(n)$ on average and $\Omega(n\log n)$ in the worst case. The last result is based on a characterization of the palindromic structure of Zimin words.
Online Computation of Abelian Runs
2015
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. We give an algorithm that finds all the abelian runs of period $\mathcal{P}$ in a word of length $n$ in time $O(n\times |\mathcal{P}|)$ and space $O(\sigma+|\mathcal{P}|)$.