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14
Tree decompositions of graphs: Saving memory in dynamic programming
- CTW 2004: Cologne-Twente Workshop on Graphs and Combinatorial Optimization, Villa Vigoni (CO
, 2004
"... We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a tree-like set covering problem. We substantiate our findings by experimental results. Our strategy has n ..."
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Cited by 10 (2 self)
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We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a tree-like set covering problem. We substantiate our findings by experimental results. Our strategy has negligible computational overhead concerning running time but achieves memory savings for nice tree decompositions and path decompositions between 60 % and 98%.
Efficient Parameterized Algorithm for Biopolymer Structure-Sequence Alignment
- In Proceedings of Workshop on Algorithms for Bioinformatics
, 2005
"... Abstract. Computational alignment of a biopolymer sequence (e.g., an RNA or a protein) to a structure is an effective approach to predict and search for the structure of new sequences. To identify the structure of remote homologs, the structure-sequence alignment has to consider not only sequence si ..."
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Cited by 8 (4 self)
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Abstract. Computational alignment of a biopolymer sequence (e.g., an RNA or a protein) to a structure is an effective approach to predict and search for the structure of new sequences. To identify the structure of remote homologs, the structure-sequence alignment has to consider not only sequence similarity but also spatially conserved conformations caused by residue interactions, and consequently is computationally intractable. It is difficult to cope with the inefficiency without compromising alignment accuracy, especially for structure search in genomes or large databases. This paper introduces a novel method and a parameterized algorithm for structuresequence alignment. Both the structure and the sequence are represented as graphs, where in general the graph for a biopolymer structure has a naturally small tree width. The algorithm constructs an optimal alignment by finding in the sequence graph the maximum valued subgraph isomorphic to the structure graph. It has the computational time complexity O(k t N 2) for the structure of N residues and its tree decomposition of width t. The parameter k, small in nature, is determined by a statistical cutoff for the correspondence between the structure and the sequence. The paper demonstrates a successful application of the algorithm to developing a fast program for RNA structural homology search. 1
Rapid ab initio Prediction of RNA Pseudoknots via Graph Tree Decomposition
, 2006
"... The prediction of RNA secondary structure including pseudoknots remains a challenge due to the intractable computation of the sequence conformation from nucleotide interactions under free energy models. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still ..."
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Cited by 8 (0 self)
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The prediction of RNA secondary structure including pseudoknots remains a challenge due to the intractable computation of the sequence conformation from nucleotide interactions under free energy models. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still require a high-degree polynomial time complexity, which is too expensive to use. Heuristic methods may yield timeefficient algorithms but they do not guarantee optimality of the predicted structure. This paper introduces a new and efficient algorithm for the prediction of RNA structure with pseudoknots for which the structure is not restricted. Novel prediction techniques are developed based on graph tree decomposition. In particular, based on a simplified energy model, stem overlapping relationships are defined with a graph, in which a specialized maximum independent set corresponds to the desired optimal structure. Such a graph is tree decomposable; dynamic programming over a tree decomposition of the graph leads to an efficient optimal algorithm. The final structure predictions are then based on re-ranking a list of suboptimal structures under a more comprehensive free energy model. The new algorithm is evaluated on a large number of RNA sequence sets taken from diverse resources. It demonstrates overall sensitivity and specificity that outperforms or is comparable with those of previous optimal and heuristic algorithms yet it requires significantly less time than the compared optimal algorithms.
Fast and Accurate Search for Non-coding RNA Pseudoknot Structures in Genomes
"... Motivation: Searching genomes for non-coding RNAs (ncRNAs) by their secondary structure has become an important goal for bioinformatics. For pseudoknot-free structures, ncRNA search can be effective based on the covariance model and CYK-type dynamic programming. However, the computational difficulty ..."
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Cited by 8 (2 self)
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Motivation: Searching genomes for non-coding RNAs (ncRNAs) by their secondary structure has become an important goal for bioinformatics. For pseudoknot-free structures, ncRNA search can be effective based on the covariance model and CYK-type dynamic programming. However, the computational difficulty in aligning an RNA sequence to a pseudoknot has prohibited fast and accurate search of arbitrary RNA structures. Our previous work introduced a graph model for RNA pseudoknots and proposed to solve the structuresequence alignment by graph optimization. Given k candidate regions in the target sequence for each of the n stems in the structure, we could compute best alignment in time O(k t n) based upon a tree width t decomposition of the structure graph. However, to implement this method to programs that can routinely perform fast yet accurate RNA pseudoknot searches, we need novel heuristics to ensure that,
New Width Parameters of Graphs
, 2012
"... The main focus of this thesis is on using the divide and conquer technique to efficiently solve graph problems that are in general intractable. We work in the field of parameterized algorithms, using width parameters of graphs that indicate the complexity inherent in the structure of the input graph ..."
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Cited by 6 (2 self)
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The main focus of this thesis is on using the divide and conquer technique to efficiently solve graph problems that are in general intractable. We work in the field of parameterized algorithms, using width parameters of graphs that indicate the complexity inherent in the structure of the input graph. We use the notion of branch decompositions of a set function introduced by Robert-son and Seymour to define three new graph parameters, boolean-width, max-imum matching-width (MM-width) and maximum induced matching-width (MIM-width). We compare these new graph width parameters to existing graph parameters by defining partial orders of width parameters. We focus on tree-width, branch-width, clique-width, module-width and rank-width, and include a Hasse diagram of these orders containing 32 graph parameters. We use the size of a maximum matching in a bipartite graph as a set function to define MM-width and show that MM-width never differs by more than a multiplicative factor 3 from tree-width. The main reason for introduc-
Rapid ab initio RNA folding including pseudoknots via graph tree decomposition
- IN PROCEEDINGS OF THE 6TH WORKSHOP ON ALGORITHMS IN BIOINFORMATICS (WABI
, 2006
"... The prediction of RNA secondary structure including pseudoknots remains a challenge due to the in-tractable computation of the sequence conformation from nucleotide interactions. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still require a high-degree p ..."
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Cited by 4 (0 self)
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The prediction of RNA secondary structure including pseudoknots remains a challenge due to the in-tractable computation of the sequence conformation from nucleotide interactions. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still require a high-degree polynomial time complexity, which is too expensive to use. Heuristic methods may yield time-efficient algorithms but they do not guarantee optimality of the predicted structure. This paper introduces a new and efficient algorithm for the prediction of RNA structure with pseudoknots for which the structure is not restricted. Novel prediction techniques are developed based on graph tree decomposition. In particular, stem overlapping relationships are defined with a graph, in which a specialized maximum independent set corresponds to the desired optimal structure. Such a graph is tree decomposable; dynamic programming over a tree decomposition of the graph leads to an efficient optimal algorithm. The new algorithm is evaluated on a large number of RNA sequence sets taken from diverse resources. It demonstrates overall sensitivity and specificity that outperforms or is comparable with those of previous optimal and heuristic algorithms yet it requires significantly less time than other optimal algorithms.
Developing Fixed-Parameter Algorithms to Solve Combinatorially Explosive Biological Problems
"... Fixed-parameter algorithms can efficiently find optimal solutions to some computationally hard (NP-hard) problems. We survey five main practical techniques to develop such algorithms. Each technique is circumstantiated by case studies of applications to biological problems. We also present other kno ..."
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Cited by 2 (0 self)
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Fixed-parameter algorithms can efficiently find optimal solutions to some computationally hard (NP-hard) problems. We survey five main practical techniques to develop such algorithms. Each technique is circumstantiated by case studies of applications to biological problems. We also present other known bioinformatics-related applications and give pointers to experimental results. Key Words: Computationally hard problems; combinatorial explosions; discrete problems; fixed-parameter tractability; optimal solutions. 1
Genome analysis RNATOPS-W: a web server for RNA structure searches of genomes
, 2009
"... Summary: RNATOPS-W is a web server to search sequences for RNA secondary structures including pseudoknots. The server accepts an annotated RNA multiple structural alignment as a structural profile and genomic or other sequences to search. It is built upon RNATOPS, a command line C++ software package ..."
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Summary: RNATOPS-W is a web server to search sequences for RNA secondary structures including pseudoknots. The server accepts an annotated RNA multiple structural alignment as a structural profile and genomic or other sequences to search. It is built upon RNATOPS, a command line C++ software package for the same purpose, in which filters to speed up search are manually selected. RNATOPS-W improves upon RNATOPS by adding the function of automatic selection of a hidden Markov model (HMM) filter and also a friendly user interface for selection of a substructure filter by the user. In addition, RNATOPS-W complements existing RNA secondary structure search web servers that either use built-in structure profiles or are not able to detect pseudoknots. RNATOPS-W inherits the efficiency of RNATOPS in detecting large, complex RNA structures. Availability: The web server RNATOPS-W is available at the web site www.uga.edu/RNA-Informatics/?f=software&p=RNATOPS-w. The underlying search program RNATOPS can be downloaded at www.uga.edu/RNA-Informatics/?f=software&p=RNATOPS. Contact:
RNATOPS-W: A Web Server for RNA Structure Searches of Genomes
"... Summary: RNATOPS-W is a web server to search sequences for RNA secondary structures including pseudoknots. The server accepts an annotated RNA multiple structural alignment as a structural profile and genomic or other sequences to search. It is built upon RNATOPS (Huang et al., 2008), a command line ..."
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Summary: RNATOPS-W is a web server to search sequences for RNA secondary structures including pseudoknots. The server accepts an annotated RNA multiple structural alignment as a structural profile and genomic or other sequences to search. It is built upon RNATOPS (Huang et al., 2008), a command line C++ software package for the same purpose, in which filters to speed up search are manually selected. RNATOPS-W improves upon RNATOPS by adding the function of automatic selection of an hidden Markov model (HMM) filter and also a friendly user interface for selection of a substructure filter by the user. In addition, RNATOPS-W complements existing RNA secondary structure search web servers that either use built-in structure profiles or are not able to detect pseudoknots. RNATOPS-W inherits the efficiency of RNATOPS in detecting large, complex RNA structures. Availability: The web server RNATOPS-W is available at website www.uga.edu/RNA-Informatics/?f=software&p=RNATOPS-w. The underlying search program RNATOPS can be downloaded at www.uga.edu/RNA-Informatics/?f=software&p=RNATOPS. Contact:
ANALYZING THE AMBIGUITY IN RNA STRUCTURE USING PROBABILISTIC APPROACH
"... ABSTRACT: RNA is the second major form of nucleic acid in human cells that play intermediary role between DNA and functional protein. Several classes of RNA's are found in cells, each with distinct function. Understanding of storage and utilization of a cell's genetic information is based ..."
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ABSTRACT: RNA is the second major form of nucleic acid in human cells that play intermediary role between DNA and functional protein. Several classes of RNA's are found in cells, each with distinct function. Understanding of storage and utilization of a cell's genetic information is based on the structure of RNA. Many experimental results have shown that RNA plays a greater role in the cells. RNA sequences contains signals at the structure level can be exploited to detect functional motifs common to all or a portion of those sequence. Different types of analysis of a structure can provide functional information in different degrees of detail. In this paper various types of RNA secondary structure representation has been discussed and in which appropriate structure has been adopted for probabilistic approach that shows un-ambiguity.
