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17
Computing common intervals of K permutations, with applications to modular decomposition of graphs
, 2008
"... We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadrat ..."
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Cited by 33 (13 self)
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We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadratic number of intervals, as well as a linear space basis of this set of common intervals. Finally, we show how our results on permutations can be used for computing the modular decomposition of graphs.
Perfect sorting by reversals is not always difficult
 IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2007
"... We propose new algorithms for computing pairwise rearrangement scenarios that conserve the combinatorial structure of genomes. More precisely, we investigate the problem of sorting signed permutations by reversals without breaking common intervals. We describe a combinatorial framework for this prob ..."
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Cited by 26 (11 self)
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We propose new algorithms for computing pairwise rearrangement scenarios that conserve the combinatorial structure of genomes. More precisely, we investigate the problem of sorting signed permutations by reversals without breaking common intervals. We describe a combinatorial framework for this problem that allows us to characterize classes of signed permutations for which one can compute, in polynomial time, a shortest reversal scenario that conserves all common intervals. In particular, we define a class of permutations for which this computation can be done in linear time with a very simple algorithm that does not rely on the classical HannenhalliPevzner theory for sorting by reversals. We apply these methods to the computation of rearrangement scenarios between permutations obtained from 16 synteny blocks of the X chromosomes of the human, mouse, and rat.
Extracting synchronous grammar rules from wordlevel alignments in linear time
 In Proceedings of the 22nd International Conference on Computational Linguistics (COLING08
, 2008
"... We generalize Uno and Yagiura’s algorithm for finding all common intervals of two permutations to the setting of two sequences with manytomany alignment links across the two sides. We show how to maximally decompose a wordaligned sentence pair in linear time, which can be used to generate all pos ..."
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Cited by 10 (1 self)
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We generalize Uno and Yagiura’s algorithm for finding all common intervals of two permutations to the setting of two sequences with manytomany alignment links across the two sides. We show how to maximally decompose a wordaligned sentence pair in linear time, which can be used to generate all possible phrase pairs or a Synchronous ContextFree Grammar (SCFG) with the simplest rules possible. We also use the algorithm to precisely analyze the maximum SCFG rule length needed to cover handaligned data from various language pairs. 1
Factorization of synchronous contextfree grammars in linear time
 In NAACL Workshop on Syntax and Structure in Statistical Translation (SSST
, 2007
"... Factoring a Synchronous ContextFree Grammar into an equivalent grammar with a smaller number of nonterminals in each rule enables synchronous parsing algorithms of lower complexity. The problem can be formalized as searching for the treedecomposition of a given permutation with the minimal branchi ..."
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Cited by 9 (5 self)
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Factoring a Synchronous ContextFree Grammar into an equivalent grammar with a smaller number of nonterminals in each rule enables synchronous parsing algorithms of lower complexity. The problem can be formalized as searching for the treedecomposition of a given permutation with the minimal branching factor. In this paper, by modifying the algorithm of Uno and Yagiura (2000) for the closely related problem of finding all common intervals of two permutations, we achieve a linear time algorithm for the permutation factorization problem. We also use the algorithm to analyze the maximum SCFG rule length needed to cover handaligned data from various language pairs. 1
Averagecase analysis of perfect sorting by reversals
, 2009
"... A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NPhard. Here we show that, despite this worstcase analysis, with probability one ..."
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Cited by 7 (4 self)
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A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NPhard. Here we show that, despite this worstcase analysis, with probability one, sorting can be done in polynomial time. Further, we find asymptotic expressions for the average length and number of reversals in commuting permutations, an interesting subclass of signed permutations. hal00354235, version 1 19 Jan 2009 1
Fully Dynamic Algorithm for Recognition and Modular Decomposition of Permutation Graphs
 ALGORITHMICA
, 2009
"... This paper considers the problem of maintaining a compact representation (O(n) space) of permutation graphs under vertex and edge modifications (insertion or deletion). That representation allows us to answer adjacency queries in O(1) time. The approach is based on a fully dynamic modular decomposit ..."
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Cited by 7 (4 self)
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This paper considers the problem of maintaining a compact representation (O(n) space) of permutation graphs under vertex and edge modifications (insertion or deletion). That representation allows us to answer adjacency queries in O(1) time. The approach is based on a fully dynamic modular decomposition algorithm for permutation graphs that works in O(n) time per edge and vertex modification. We thereby obtain a fully dynamic algorithm for the recognition of permutation graphs.
A more efficient algorithm for perfect sorting by reversals
, 2008
"... We describe a new algorithm for the problem of perfect sorting a signed permutation by reversals. The worstcase time complexity of this algorithm is parameterized by the maximum prime degree d of the strong interval tree, i.e. f(d).n O(1). This improves the best known algorithm which complexity was ..."
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Cited by 6 (6 self)
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We describe a new algorithm for the problem of perfect sorting a signed permutation by reversals. The worstcase time complexity of this algorithm is parameterized by the maximum prime degree d of the strong interval tree, i.e. f(d).n O(1). This improves the best known algorithm which complexity was based on a parameter always larger than or equal to d.
Homogeneity vs. adjacency: generalising some graph decomposition algorithms
 In 32nd International Workshop on GraphTheoretic Concepts in Computer Science (WG), volume 4271 of LNCS
, 2006
"... Abstract. In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usu ..."
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Cited by 6 (2 self)
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Abstract. In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular decomposition of directed graphs and of 2structures, but also decomposition by star cutsets. 1
Soft Syntactic Constraints for Hierarchical Phrasebased Translation Using Latent Syntactic Distributions
"... In this paper, we present a novel approach to enhance hierarchical phrasebased machine translation systems with linguistically motivated syntactic features. Rather than directly using treebank categories as in previous studies, we learn a set of linguisticallyguided latent syntactic categories aut ..."
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Cited by 4 (1 self)
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In this paper, we present a novel approach to enhance hierarchical phrasebased machine translation systems with linguistically motivated syntactic features. Rather than directly using treebank categories as in previous studies, we learn a set of linguisticallyguided latent syntactic categories automatically from a sourceside parsed, wordaligned parallel corpus, based on the hierarchical structure among phrase pairs as well as the syntactic structure of the source side. In our model, each X nonterminal in a SCFG rule is decorated with a realvalued feature vector computed based on its distribution of latent syntactic categories. These feature vectors are utilized at decoding time to measure the similarity between the syntactic analysis of the source side and the syntax of the SCFG rules that are applied to derive translations. Our approach maintains the advantages of hierarchical phrasebased translation systems while at the same time naturally incorporates soft syntactic constraints.
Enumeration of Factorizable MultiDimensional Permutations
"... A ddimensional permutation is a sequence of d + 1 permutations with the leading element being the identity permutation. It can be viewed as an alignment structure across d+1 sequences, or visualized as the result of permuting n hypercubes of (d+1) dimensions. We study the hierarchical decomposition ..."
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Cited by 1 (1 self)
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A ddimensional permutation is a sequence of d + 1 permutations with the leading element being the identity permutation. It can be viewed as an alignment structure across d+1 sequences, or visualized as the result of permuting n hypercubes of (d+1) dimensions. We study the hierarchical decomposition of ddimensional permutations. We show that when d ≥ 2, the ratio between nondecomposable or simple dpermutations and all dpermutations approaches 1. We also prove that the growth rate of the number of dpermutations that can be factorized into kary branching trees approaches � � k d e as k grows. 1