An Algorithm for the Modular Decomposition of Hypergraphs

Algorithmic aspects of switch cographs

A general algorithmic scheme for combinatorial decompositions with application to modular decompositions of hypergraphs

A fully dynamic algorithm for modular decomposition and recognition of cographs

The first polynomial time algorithm (\(\mathcal{O}(n^4)\)) for modular decomposition appeared in 1972 [8] and since then there have been incremental improvements, eventually resulting in linear-time algorithms [22,7,23,9]. Although having optimal time complexity these algorithms are quite complicated and difficult to implement. In this paper we present an easily implementable linear-time algorithm for modular decomposition. This algorithm uses the notion of factorizing permutation and a new data-structure, the Ordered Chain Partitions.KeywordsInterval GraphDecomposition TreeRecursive CallStrong ModuleChordal GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The facets of the polytope of modules of a graph

Fully dynamic representations of interval graphs

Counting spanning trees using modular decomposition

Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem. We benchmark their performance as well as that of the commonly-used greedy search on physically relevant tensor networks. Where computationally feasible, we also compare them with the optimal contraction sequence obtained by an exhaustive search. Furthermore, we present a systematic comparison with state-of-the-art tree decomposition and graph partitioning algorithms in the context of random regular graph tensor networks. We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.

Representation of Quad Tree Decomposition and Various Segmentation Algorithms in Information Bottleneck Method

In order to overcome the problem that the existing scheme is difficult to adapt to the network link additions and deletions to the situation, this paper proposes a link fault localization scheme based on tree decomposition. Firstly, a multi degree lossless image segmentation algorithm is proposed to divide the network into several independent sub networks. Secondly, the maximum width priority tree decomposition algorithm is proposed to generate multi loop in the sub graph. The average number of links and the total delay of the proposed algorithm are better than that of the genetic algorithm. Experiments show that the number of indicators such as static flows in the schema needed to be sent to the table and detection information needed to be sent to detect link faults is superior than the existing programs.

Differential transcript expression (DTE) analysis without predefined conditions is critical to biological studies. For example, it can be used to discover biomarkers to classify cancer samples into previously unknown subtypes such that better diagnosis and therapy methods can be developed for the subtypes. Although several DTE tools for population data, i.e. data without known biological conditions, have been published, these tools either assume binary conditions in the input population or require the number of conditions as a part of the input. Fixing the number of conditions to binary is unrealistic and may distort the results of a DTE analysis. Estimating the correct number of conditions in a population could also be challenging for a routine user. Moreover, the existing tools only provide differential usages of exons, which may be insufficient to interpret the patterns of alternative splicing across samples and restrains the applications of the tools from many biology studies. We propose a novel DTE analysis algorithm, called SDEAP, that estimates the number of conditions directly from the input samples using a Dirichlet mixture model and discovers alternative splicing events using a new graph modular decomposition algorithm. By taking advantage of the above technical improvement, SDEAP was able to outperform the other DTE analysis methods in our extensive experiments on simulated data and real data with qPCR validation. The prediction of SDEAP also allowed us to classify the samples of cancer subtypes and cell-cycle phases more accurately. SDEAP is publicly available for free at https://github.com/ewyang089/SDEAP/wiki CONTACT: yyang027@cs.ucr.edu; jiang@cs.ucr.eduSupplementary information: Supplementary data are available at Bioinformatics online.

We prove a characterization of all polynomial-time computable queries on the class of interval graphs by sentences of fixed-point logic with counting. More precisely, it is shown that on the class of unordered interval graphs, any query is polynomial-time computable if and only if it is definable in fixed-point logic with counting. This result is one of the first establishing the capturing of polynomial time on a graph class which is defined by forbidden induced subgraphs. For this, we define a canonical form of interval graphs using a type of modular decomposition, which is different from the method of tree decomposition that is used in most known capturing results for other graph classes, specifically those defined by forbidden minors. The method might also be of independent interest for its conceptual simplicity. Furthermore, it is shown that fixed-point logic with counting is not expressive enough to capture polynomial time on the classes of chordal graphs or incomparability graphs.

Determination of side-chain conformations is an important step in protein structure prediction and protein design. Many such methods have been presented, although only a small number are in widespread use. SCWRL is one such method, and the SCWRL3 program (2003) has remained popular because of its speed, accuracy, and ease-of-use for the purpose of homology modeling. However, higher accuracy at comparable speed is desirable. This has been achieved in a new program SCWRL4 through: (1) a new backbone-dependent rotamer library based on kernel density estimates; (2) averaging over samples of conformations about the positions in the rotamer library; (3) a fast anisotropic hydrogen bonding function; (4) a short-range, soft van der Waals atom-atom interaction potential; (5) fast collision detection using k-discrete oriented polytopes; (6) a tree decomposition algorithm to solve the combinatorial problem; and (7) optimization of all parameters by determining the interaction graph within the crystal environment using symmetry operators of the crystallographic space group. Accuracies as a function of electron density of the side chains demonstrate that side chains with higher electron density are easier to predict than those with low-electron density and presumed conformational disorder. For a testing set of 379 proteins, 86% of chi(1) angles and 75% of chi(1+2) angles are predicted correctly within 40 degrees of the X-ray positions. Among side chains with higher electron density (25-100th percentile), these numbers rise to 89 and 80%. The new program maintains its simple command-line interface, designed for homology modeling, and is now available as a dynamic-linked library for incorporation into other software programs.

Epistasis is an important factor affecting complex disease, some powerful methods should be proposed in order to improve large-scale genome-wide data mining efficiency. There are some problems exist in epistasis detection methods, such as low efficiency, low accuracy and inability to process large number of SNPs. In this work, we propose a k-tree optimizing Bayesian network (BN) epistasis mining method that can deal with large-scale of SNPs. Firstly, we construct the k-tree including large-scale of SNP loci and phenotype traits by sampling the Dandelion code uniformly. Then the k-tree is decomposed into different k-cliques by using the degree selection tree decomposition algorithm. In different k-cliques, the optimized fast incremental association BN learning method (omb-Fast) is used to learn the sub-Bayesian network quickly and accurately. Finally, all the sub-networks are merged to obtain the whole network. The above operations (k-tree generation, k-tree decomposition, network generation) are done several times, and thus to obtain the epistatic loci affecting phenotype traits. The simulated experiments validate the effective of our method. Experiment results show that the proposed method has better epistasis detection accuracy, lower false positive rate and higher F1-score on the basis of ensuring the efficiency compared to other methods. Most importantly, it can be used into large-scale of SNPs in the whole-genome for epistasis detection.

In order to accurately decompose the surface morphology of machined surface and trace the potential errors of the machine, a comprehensive improved algorithm is proposed, which combines wavelet packet decomposition (WPD) and improved complete ensemble empirical modal decomposition of adaptive noise (Improve CEEMDAN). Firstly, the cost function is used to find the optimal wavelet packet base and the optimal decomposition tree is obtained. Secondly, under semi-hard threshold denoising, the wavelet coefficients obtained by the optimal decomposition tree can generate the denoised signal. Finally, the white noise is preprocessed to obtain the upper limit frequency and the band white noise, and the improvement of CEEMDAN is completed. The improved CEEMDAN is used to decompose the denoised signal to obtain a series of intrinsic mode functions (IMFs). The merit of this comprehensive improved algorithm is that it can improve the calculation efficiency and decomposition accuracy by adaptively finding the optimal wavelet packet base and adding band-limited white noise. Simulations and experiments results show the feasibility, effectiveness and higher accuracy of the comprehensive algorithm in decomposing surface topography.