37155625
Efficient Parameterized Algorithm for Biopolymer Structure-Sequence Alignment
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 structure-sequence 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.
41440512
Polynomial Time Approximation Schemes and Parameterized Complexity
10668543
Parameterized Computation of LCS for Two Sequences
The problem of finding the longest common subsequence is a well-known optimization problem because of its applications, especially in bioinformatics. In this paper, by applying the techniques developed in parameterized computation, an efficient approach for the problem of finding the longest common subsequence of two sequences is presented. The parameterized approach is compared with the well-known dynamic programming approach for the problem. The parameterized approach is much more efficient, as is shown by the experimental results.
2661456
Linear FPT reductions and computational lower bounds
We develop new techniques for deriving very strong computational lower bounds for a class of well-known NP-hard problems, including weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(nk) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the problem is not solvable in time f(k) no(k) for any function f, even if we restrict the parameter value k to be bounded by an arbitrarily small function of n. Under the same assumption, we prove that even if we restrict the parameter values k to be Θ(μ(n)) for any reasonable function μ, no algorithm of running time no(k) can test if a graph of n vertices has a clique of size k. Similar strong lower bounds are also derived for other problems in the above class. Our techniques can be extended to derive computational lower bounds on approximation algorithms for NP-hard optimization problems. For example, we prove that the NP-hard distinguishing substring selection problem, for which a polynomial time approximation scheme has been recently developed, has no polynomial time approximation schemes of running time f(1/ε)no(1/ε) for any function f unless an unlikely collapse occurs in parameterized complexity theory.
15028779
W-Hardness Under Linear FPT-Reductions: Structural Properties and Further Applications
The notion of linear fpt-reductions has been recently used to derive strong computational lower bounds for well-known NP-hard problems. In this paper, we formally investigate the notions of W[t]-hardness and W[t]-completeness under the linear fpt-reduction, and study structural properties of the corresponding complexity classes. Additional complexity lower bounds on important computational problems are also established.
38436825
Fixed-Parameter Approximation: Conceptual Framework and Approximability Results
The notion of fixed-parameter approximation is introduced to investigate the approximability of optimization problems within the framework of fixed-parameter computation. This work partially aims at enhancing the world of fixed-parameter computation in parallel with the conventional theory of computation that includes both exact and approximate computations. In particular, it is proved that fixed-parameter approximability is closely related to the approximation of small-cost solutions in polynomial time. It is also demonstrated that many fixed-parameter intractable problems are not fixed-parameter approximable. On the other hand, fixed-parameter approximation appears to be a viable approach to solving some inapproximable yet important optimization problems. For instance, all problems in the class MAX SNP admit fixed-parameter approximation schemes in time O(2$^{O((1-{\epsilon}/{\it O}(1)){\it k})}$p(n)) for any small e> 0.
18862916
Clustering graphs for visualization via node similarities
Graph visualization is commonly used to visually model relations in many areas. Examples include Web sites, CASE tools, and knowledge representation. When the amount of information in these graphs becomes too large, users, however, cannot perceive all elements at the same time. A clustered graph can greatly reduce visual complexity by temporarily replacing a set of nodes in clusters with abstract nodes. This paper proposes a new approach to clustering graphs. The approach constructs the node similarity matrix of a graph that is derived from a novel metric of node similarity. The linkage pattern of the graph is thus encoded into the similarity matrix, and then one obtains the hierarchical abstraction of densely linked subgraphs by applying the k-means algorithm to the matrix. A heuristic method is developed to overcome the inherent drawbacks of the k-means algorithm. For clustered graphs we present a multilevel multi-window approach to hierarchically drawing them in different abstract level views with the purpose of improving their readability. The proposed approaches demonstrate good results in our experiments. As application examples, visualization of part of Java class diagrams and Web graphs are provided. We also conducted usability experiments on our algorithm and approach. The results have shown that the hierarchically clustered graph used in our system can improve user performance for certain types of tasks.
5775998
Identification of clusters in the Web graph based on link topology
The Web graph has recently been used to model the link structure of the Web. The studies of such graphs can yield valuable insights into Web algorithms for crawling, searching and discovery of Web communities. This paper proposes a new approach to clustering the Web graph. The proposed algorithm identifies a small subset of the graph as "core" members of clusters, and then incrementally constructs the clusters by a selection criterion. Two qualitative criteria are proposed to measure the quality of graph clustering. We have implemented our algorithm and tested a set of arbitrary graphs with good results. Applications of our approach include graph drawing and Web visualization.
10876880
Multimedia materials for teaching signal processing
Rapidly advancing capabilities in PC-based multimedia technology are providing new opportunities for delivery of educational material. Multimedia technology is being introduced at all levels of the degrees in Electronics and Communications at the University of New England (UNE). In this paper attention is drawn the use of multimedia technology through the example of a fourth-year education package on signal processing. We have used this multimedia education package for teaching and learning during formal class periods and to encourage students to use the technology in their own personal study and projects in order to increase their engineering generic skills. The success of the venture has encouraged us to extend the technology to other selected units in the UNE engineering programs.
9602783
Discovery of interesting association rules from Livelink web log data
We present our experience in mining web usage patterns from a large collection of Livelink log data. Livelink is a web-based product of Open Text, which provides automatic management and retrieval of different types of information objects over an intranet or extranet. We report our experience in preprocessing raw log data and post-processing the mining results for finding interesting rules. In particular we compare and evaluate a number of rule interestingness measures and find that two of the measures that have not been used in association rule learning work very well.
621625
Image noise removal in Nakagami fading channels via Bayesian estimator
A maximum likelihood for Bayesian estimator based on alpha-stable was discussed in our previous papers. It is in terms of closer to a realistic situation, and unlike previous methods used for Bayesian estimator, for the case discussed here it is not necessary to know the variance of the noise. The Bayesian estimator here is based on in a Nakagami fading channel. Our previous research results has been extended to that Bayesian estimator that we investigated is still working well for the image noise removal in Nakagami fading channels. As an example, an improved Bayesian estimator (soft and hard threshold methods), is illustrated in our discussion