Results 1  10
of
14
Tree decompositions of graphs: Saving memory in dynamic programming
 CTW 2004: CologneTwente 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 treelike set covering problem. We substantiate our findings by experimental results. Our strategy has n ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
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 treelike 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 StructureSequence 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 structuresequence alignment has to consider not only sequence si ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
(Show Context)
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 structuresequence 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 ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
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 highdegree 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 reranking 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 Noncoding RNA Pseudoknot Structures in Genomes
"... Motivation: Searching genomes for noncoding RNAs (ncRNAs) by their secondary structure has become an important goal for bioinformatics. For pseudoknotfree structures, ncRNA search can be effective based on the covariance model and CYKtype dynamic programming. However, the computational difficulty ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
Motivation: Searching genomes for noncoding RNAs (ncRNAs) by their secondary structure has become an important goal for bioinformatics. For pseudoknotfree structures, ncRNA search can be effective based on the covariance model and CYKtype 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 ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
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 Robertson and Seymour to define three new graph parameters, booleanwidth, maximum matchingwidth (MMwidth) and maximum induced matchingwidth (MIMwidth). We compare these new graph width parameters to existing graph parameters by defining partial orders of width parameters. We focus on treewidth, branchwidth, cliquewidth, modulewidth and rankwidth, 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 MMwidth and show that MMwidth never differs by more than a multiplicative factor 3 from treewidth. 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 intractable 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 highdegree p ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
The prediction of RNA secondary structure including pseudoknots remains a challenge due to the intractable 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 highdegree 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, 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 FixedParameter Algorithms to Solve Combinatorially Explosive Biological Problems
"... Fixedparameter algorithms can efficiently find optimal solutions to some computationally hard (NPhard) 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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Fixedparameter algorithms can efficiently find optimal solutions to some computationally hard (NPhard) 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 bioinformaticsrelated applications and give pointers to experimental results. Key Words: Computationally hard problems; combinatorial explosions; discrete problems; fixedparameter tractability; optimal solutions. 1
Genome analysis RNATOPSW: a web server for RNA structure searches of genomes
, 2009
"... Summary: RNATOPSW 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 ..."
Abstract
 Add to MetaCart
Summary: RNATOPSW 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. RNATOPSW 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, RNATOPSW complements existing RNA secondary structure search web servers that either use builtin structure profiles or are not able to detect pseudoknots. RNATOPSW inherits the efficiency of RNATOPS in detecting large, complex RNA structures. Availability: The web server RNATOPSW is available at the web site www.uga.edu/RNAInformatics/?f=software&p=RNATOPSw. The underlying search program RNATOPS can be downloaded at www.uga.edu/RNAInformatics/?f=software&p=RNATOPS. Contact:
RNATOPSW: A Web Server for RNA Structure Searches of Genomes
"... Summary: RNATOPSW 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 ..."
Abstract
 Add to MetaCart
(Show Context)
Summary: RNATOPSW 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. RNATOPSW 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, RNATOPSW complements existing RNA secondary structure search web servers that either use builtin structure profiles or are not able to detect pseudoknots. RNATOPSW inherits the efficiency of RNATOPS in detecting large, complex RNA structures. Availability: The web server RNATOPSW is available at website www.uga.edu/RNAInformatics/?f=software&p=RNATOPSw. The underlying search program RNATOPS can be downloaded at www.uga.edu/RNAInformatics/?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 ..."
Abstract
 Add to MetaCart
(Show Context)
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 unambiguity.