Search results for "data structures"
showing 10 items of 258 documents
Text Compression Using Antidictionaries
1999
International audience; We give a new text compression scheme based on Forbidden Words ("antidictionary"). We prove that our algorithms attain the entropy for balanced binary sources. They run in linear time. Moreover, one of the main advantages of this approach is that it produces very fast decompressors. A second advantage is a synchronization property that is helpful to search compressed data and allows parallel compression. Our algorithms can also be presented as "compilers" that create compressors dedicated to any previously fixed source. The techniques used in this paper are from Information Theory and Finite Automata.
Automata and forbidden words
1998
Abstract Let L ( M ) be the (factorial) language avoiding a given anti-factorial language M . We design an automaton accepting L ( M ) and built from the language M . The construction is effective if M is finite. If M is the set of minimal forbidden words of a single word ν, the automaton turns out to be the factor automaton of ν (the minimal automaton accepting the set of factors of ν). We also give an algorithm that builds the trie of M from the factor automaton of a single word. It yields a nontrivial upper bound on the number of minimal forbidden words of a word.
Minimal forbidden words and factor automata
1998
International audience; Let L(M) be the (factorial) language avoiding a given antifactorial language M. We design an automaton accepting L(M) and built from the language M. The construction is eff ective if M is finite. If M is the set of minimal forbidden words of a single word v, the automaton turns out to be the factor automaton of v (the minimal automaton accepting the set of factors of v). We also give an algorithm that builds the trie of M from the factor automaton of a single word. It yields a non-trivial upper bound on the number of minimal forbidden words of a word.
$O(n^2 log n)$ Time On-line Construction of Two-Dimensional Suffix Trees
2007
The two-dimensional suffix tree of an n × n square matrix A is a compacted trie that represents all square submatrices of A [11]. For the off-line case, i.e., A is given in advance to the algorithm, it is known how to build it in optimal time, for any type of alphabet size [11], [18]. Motivated by applications in Image Compression [22], Giancarlo and Guaiana [14] considered the on-line version of the two-dimensional suffix tree and presented an O(n2 log2 n)-time algorithm, which we refer to as GG. That algorithm is a nontrivial generalization of Ukkonen’s on-line algorithm for standard suffix trees [23]. The main contribution in this paper is an O(logn) factor improvement in the time comple…
Distributed Leader Election and Computation of Local Identifiers for Programmable Matter
2019
International audience; The context of this paper is programmable matter, which consists of a set of computational elements, called particles, in an infinite graph. The considered infinite graphs are the square, triangular and king grids. Each particle occupies one vertex, can communicate with the adjacent particles, has the same clockwise direction and knows the local positions of neighborhood particles. Under these assumptions, we describe a new leader election algorithm affecting a variable to the particles, called the k-local identifier, in such a way that particles at close distance have each a different k-local identifier. For all the presented algorithms, the particles only need a O(…
Decremental 2- and 3-connectivity on planar graphs
1996
We study the problem of maintaining the 2-edge-, 2-vertex-, and 3-edge-connected components of a dynamic planar graph subject to edge deletions. The 2-edge-connected components can be maintained in a total ofO(n logn) time under any sequence of at mostO(n) deletions. This givesO(logn) amortized time per deletion. The 2-vertex- and 3-edge-connected components can be maintained in a total ofO(n log2n) time. This givesO(log2n) amortized time per deletion. The space required by all our data structures isO(n). All our time bounds improve previous bounds.
Lightweight LCP construction for next-generation sequencing datasets
2012
The advent of "next-generation" DNA sequencing (NGS) technologies has meant that collections of hundreds of millions of DNA sequences are now commonplace in bioinformatics. Knowing the longest common prefix array (LCP) of such a collection would facilitate the rapid computation of maximal exact matches, shortest unique substrings and shortest absent words. CPU-efficient algorithms for computing the LCP of a string have been described in the literature, but require the presence in RAM of large data structures. This prevents such methods from being feasible for NGS datasets. In this paper we propose the first lightweight method that simultaneously computes, via sequential scans, the LCP and B…
Toward a virtual reconstruction of an antique three-dimensional marble puzzle
2017
International audience; Abstract | Introduction | Related Work | Acquisition Setup, Proposed Prototype: Calibration and Visibility | Preprocessing of Scanned Three-Dimensional Fragment Data | Processing of Scanned Three-Dimensional Surface Data: Matching | Conclusion and Future Works | Appendices | Acknowledgments | ReferencesAbstract. The reconstruction of broken objects is an important field of research for many applications, such as art restoration, surgery, forensics, and solving puzzles. In archaeology, the reconstruction of broken artifacts is a very time-consuming task due to the handling of fractured objects, which are generally fragile. However, it can now be supported by three-dim…
Bords d'une surface médiane : Identifications et applications
2014
National audience; Un squelette d'une forme fermée est une structure mince, centrée dans cette forme, décrivant sa topologie et sa géométrie. Les squelettes permettent de développer des applications interactives en synthèse d'images~: l'utilisateur peut manipuler intuitivement des formes en modifiant leurs squelettes. Parmi toutes les formulations de squelettes, nous nous intéressons en particulier à la surface médiane. Ses éléments, nommés atomes, sont les sphères maximales intérieures à la forme décrite. Les positions des atomes sont organisées en courbes et surfaces, qui composent la structure squelettale. Cette structure peut être d'une grande aide pour manipuler une forme. Cependant, e…
WSN localization scheme based on Received Signal Strength Indicator (RSSI) for ZigBee Networks
2015
International audience; Wireless Sensor Networks (WSNs) have diverse application domains such as smart home, smart care, industrial, etc. We present a WSN system based on the ZigBee technology (IEEE 802.15.4) in Smart Home. In our paper we interest to ZigBee protocol is often used in medical Rehabilitation, which is a relatively new concept involving wireless transmission of data from the sensors attached to a patient to a distant monitoring station. There is no standardized topology managing the current networks, therefore, we will compare and evaluate the performance the mobility of nodes for star topologies in different scenarios to determine which is the most suitable in a typical hospi…