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Comparing rna structures: towards an intermediate model between the edit and the lapcs problems
 In MarieFrance Sagot
, 2007
"... Abstract. In the recent past, RNA structure comparison has appeared as an important field of bioinformatics. In this paper, we introduce a new and general intermediate model for comparing RNA structures: the Maximum ArcPreserving Common Subsequence problem (or Mapcs). This new model lies between tw ..."
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Abstract. In the recent past, RNA structure comparison has appeared as an important field of bioinformatics. In this paper, we introduce a new and general intermediate model for comparing RNA structures: the Maximum ArcPreserving Common Subsequence problem (or Mapcs). This new model lies between two wellknown problems – namely the Longest ArcPreserving Common Subsequence (Lapcs) and the Edit distance. After showing the relationship between Mapcs, Lapcs, Edit, and also the Maximum Linear Graph problem, we will investigate the computational complexity landscape of Mapcs, depending on the RNA structure complexity.
Common Structured Patterns in Linear Graphs: Approximations and Combinatorics
"... A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (⊏) or crossing (≬). Given a family of linear graphs, and a nonempty subset R ⊆ {<, ⊏, ≬} of these three relations, we are interested in the M ..."
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Cited by 2 (1 self)
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A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (⊏) or crossing (≬). Given a family of linear graphs, and a nonempty subset R ⊆ {<, ⊏, ≬} of these three relations, we are interested in the Maximum Common Structured Pattern (MCSP) problem: Find a maximum size edgedisjoint graph, with edgepairs all comparable by one of the relations in R, that occurs as a subgraph in each of the linear graphs of the family. In this paper, we generalize the framework of Davydov and Batzoglou by considering patterns comparable by all possible subsets R ⊆ {<, ⊏, ≬}. This is motivated by the fact that many biological applications require considering crossing structures, and by the fact that different combinations of the relations above give rise to different generalizations of natural combinatorial problems. Our results can be summarized as follows: We give tight hardness results for the MCSP problem for {<, ≬}structured patterns and {⊏, ≬}structured patterns. Furthermore, we prove that the problem is approximable within ratios: (i) 2H (k) for {<, ≬}structured patterns, (ii) k 1/2 for {⊏, ≬}structured patterns, and (iii) O ( √ k lg k) for {<, ⊏, ≬}structured patterns, where k is the size of the optimal solution and H (k) = �k i=1 1/i is the kth harmonic number. Along the way, we provide combinatorial results concerning the different types of structured patterns that are of independent interest in their own right.
LONGEST COMMON SEPARABLE PATTERN BETWEEN PERMUTATIONS
, 2007
"... Abstract. In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomialtime algorithm when the number of input permutations is fixed and show that the problem is NPhard for an arbitrary number of input permutations even if ..."
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Abstract. In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomialtime algorithm when the number of input permutations is fixed and show that the problem is NPhard for an arbitrary number of input permutations even if these permutations are separable. On the other hand, we show that the NPhard problem of finding the longest common pattern between two permutations cannot be approximated better than within a ratio of √ Opt (where Opt is the size of an optimal solution) when taking common patterns belonging to patternavoiding classes of permutations. 1. Introduction and
Comparing RNA Structures: Towards an Intermediate Model Between the Edit and the Lapcs Problems
, 2013
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Finding Common Structured Patterns in Linear Graphs
, 2009
"... A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (⊏) or crossing (≬). Given a family of linear graphs, and a nonempty subset R ⊆ {<, ⊏, ≬}, we are interested in the Maximum Common Structured ..."
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A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (⊏) or crossing (≬). Given a family of linear graphs, and a nonempty subset R ⊆ {<, ⊏, ≬}, we are interested in the Maximum Common Structured Pattern (MCSP) problem: find a maximum size edgedisjoint graph, with edgepairs all comparable by one of the relations in R, that occurs as a subgraph in each of the linear graphs of the family. The MCSP problem generalizes many structurecomparison and structureprediction problems that arise in computational molecular biology. We give tight hardness results for the MCSP problem for {<, ≬}structured patterns and {⊏, ≬}structured patterns. Furthermore, we prove that the problem is approximable within ratios: (i) 2H (k) for {<, ≬}structured patterns, (ii) k1/2 for {⊏, ≬}structured patterns, and (iii) O ( √ k log k) for {<, ⊏, ≬}structured patterns, where k is the size of the optimal solution and H (k) = ∑k i=1
To cite this version:
, 2009
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Averagecase analysis of perfect sorting by reversals