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Reflections on multivariate algorithmics and problem parameterization
 PROC. 27TH STACS
, 2010
"... Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and e ..."
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Research on parameterized algorithmics for NPhard problems has steadily grown over the last years. We survey and discuss how parameterized complexity analysis naturally develops into the field of multivariate algorithmics. Correspondingly, we describe how to perform a systematic investigation and exploitation of the “parameter space” of computationally hard problems.
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 ..."
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Cited by 8 (2 self)
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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,
Exploiting bounded signal flow for graph orientation based on causeeffect pairs
 In Proceedings of the 1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems (TAPAS 2011
"... Background: We consider the following problem: Given an undirected network and a set of sender–receiver pairs, direct all edges such that the maximum number of “signal flows ” defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein intera ..."
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Background: We consider the following problem: Given an undirected network and a set of sender–receiver pairs, direct all edges such that the maximum number of “signal flows ” defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein interaction based cell regulation mechanisms. Since this problem is NPhard, research so far concentrated on polynomialtime approximation algorithms and tractable special cases. Results: We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixedparameter tractability results, and in one case a sharp complexity dichotomy between a lineartime solvable case and a slightly more general NPhard case. We examine the value of these parameters for several realworld network instances. Conclusions: Several biologically relevant special cases of the NPhard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies. Background Current technologies [1] like twohybrid screening can
On the Ordered List Subgraph Embedding Problems
"... Abstract. In the (parameterized) Ordered List Subgraph Embedding problem (pOLSE) we are given two graphs G and H, each with a linear order defined on its vertices, a function L that associates with every vertex in G a list of vertices in H, and a parameter k. The question is to decide if we can emb ..."
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Abstract. In the (parameterized) Ordered List Subgraph Embedding problem (pOLSE) we are given two graphs G and H, each with a linear order defined on its vertices, a function L that associates with every vertex in G a list of vertices in H, and a parameter k. The question is to decide if we can embed (onetoone) a subgraph S of G of cardinality k into H such that: (1) every vertex of S is mapped to a vertex from its associated list, (2) the linear orders inherited by S and its image under the embedding are respected, and (3) if there is an edge between two vertices in S then there is an edge between their images. If we require the subgraph S to be embedded as an induced subgraph, we obtain the Ordered List Induced Subgraph Embedding problem (pOLISE). The pOLSE and pOLISE problems model various problems in Bioinformatics related to structural comparison/alignment of proteins. We investigate the complexity of pOLSE and pOLISE with respect to the following structural parameters: the width ∆L of the function L (size of the largest list), and the maximum degree ∆H of H and ∆G of G. We provide tight characterizations of the classical and parameterized complexity, and approximability of the problems with respect to the structural parameters under consideration.
Treewidth and Hypertree Width
, 2014
"... The chapter covers methods for identifying islands of tractability for NPhard combinatorial problems by exploiting suitable properties of their graphical structure. Acyclic structures are considered, as well as nearly acyclic ones identified by means of socalled structural decomposition methods. ..."
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The chapter covers methods for identifying islands of tractability for NPhard combinatorial problems by exploiting suitable properties of their graphical structure. Acyclic structures are considered, as well as nearly acyclic ones identified by means of socalled structural decomposition methods. In particular, the chapter focuses on the tree decomposition method, which is the most powerful decomposition method for graphs, and on the hypertree decomposition method, which is its natural counterpart for hypergraphs. These problemdecomposition methods give rise to corresponding notions of width of an instance, namely, treewidth and hypertree width. It turns out that many NPhard problems can be solved efficiently over classes of instances of bounded treewidth or hypertree width: deciding whether a solution exists, computing a solution, and even computing an optimal solution (if some cost function over solutions is specified) are all polynomialtime tasks. Example applications include problems from artificial intelligence, databases, game theory, and combinatorial auctions.
A New Approach for Parameter Estimation in the Sequencestructure Alignment of Noncoding RNAs
"... Recently, searching genomes with a computer program has become an important approach for identifying new noncoding RNAs (ncRNA). Such a computer program often determines whether a sequence segment is the searched ncRNA or not by aligning the sequence segment to a secondary structure model for the se ..."
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Recently, searching genomes with a computer program has become an important approach for identifying new noncoding RNAs (ncRNA). Such a computer program often determines whether a sequence segment is the searched ncRNA or not by aligning the sequence segment to a secondary structure model for the searched ncRNA family. To a large extent, the search accuracy depends on the accuracy of the secondary structure model. In this paper, we develop a novel algorithm that can estimate the parameters associated with a few crucial structure features that have been proposed in previous work. This algorithm determines the relative importance of the crucial structure features by solving a convex optimization problem whose objective is to maximize the recognition ability of the structure model. Our experiments also show that this new parameter estimation algorithm can significantly improve the search accuracy.
A New Parameterized Algorithm for Rapid Peptide Sequencing
, 2014
"... De novo sequencing is an important computational approach to determining the amino acid sequence of a peptide with tandem mass spectrometry (MS/MS). Most of the existing approaches use a graph model to describe a spectrum and the sequencing is performed by computing the longest antisymmetric path in ..."
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De novo sequencing is an important computational approach to determining the amino acid sequence of a peptide with tandem mass spectrometry (MS/MS). Most of the existing approaches use a graph model to describe a spectrum and the sequencing is performed by computing the longest antisymmetric path in the graph. The task is often computationally intensive since a given MS/MS spectrum often contains noisy data, missing mass peaks, or post translational modifications/ mutations. This paper develops a new parameterized algorithm that can efficiently compute the longest antisymmetric partial path in an extended spectrum graph that is of bounded path width. Our testing results show that this algorithm can efficiently process experimental spectra and provide sequencing results of high accuracy.