Abstract. 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. Key words. common interval, permutation, PQ-tree, modular decomposition AMS subject classifications. 05C05, 05C62, 68R99

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 Hannenhalli-Pevzner 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.

Factoring a Synchronous Context-Free 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 tree-decomposition 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 hand-aligned data from various language pairs. 1

We generalize Uno and Yagiura’s algorithm for finding all common intervals of two permutations to the setting of two sequences with many-to-many alignment links across the two sides. We show how to maximally decompose a word-aligned sentence pair in linear time, which can be used to generate all possible phrase pairs or a Synchronous Context-Free Grammar (SCFG) with the simplest rules possible. We also use the algorithm to precisely analyze the maximum SCFG rule length needed to cover hand-aligned data from various language pairs. 1

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.

We describe a new algorithm for the problem of perfect sorting a signed permutation by reversals. The worst-case 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.

In this paper, we present a novel approach to enhance hierarchical phrase-based machine translation systems with linguistically motivated syntactic features. Rather than directly using treebank categories as in previous studies, we learn a set of linguistically-guided latent syntactic categories automatically from a source-side parsed, word-aligned 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 real-valued 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 phrase-based translation systems while at the same time naturally incorporates soft syntactic constraints.

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 2-structures, but also decomposition by star cutsets. 1

A d-dimensional 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 d-dimensional permutations. We show that when d ≥ 2, the ratio between non-decomposable or simple d-permutations and all d-permutations approaches 1. We also prove that the growth rate of the number of d-permutations that can be factorized into k-ary branching trees approaches � � k d e as k grows. 1

In this paper, we give a polynomial (O(n 8)) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general permutations whose complexity depends on the length of the longest simple permutation involved in one of our permutations. 1 Introduction and basic concepts The study of patterns in permutations has blossomed these last years: from a combinatorial point of view with the recent proof of the Stanley-Wilf conjecture by Marcus and Tardös, and from an algorithmic one with the development of algorithms for pattern and general pattern involvement. Although the general