Backtracking combined with branching heuristics is a prevalent approach for tackling constraint satisfaction problems (CSPs) and combinatorial optimization problems (COPs). While branching heuristics specifically designed for certain problems can be theoretically efficient, they are often complex and difficult to implement in practice. On the other hand, general branching heuristics can be applied across various problems, but at the risk of suboptimality. We introduce a solver framework that leverages the Shannon entropy in branching heuristics to bridge the gap between generality and specificity in branching heuristics. This enables backtracking to follow the path of least uncertainty, based on probability distributions that conform to problem constraints. We employ graph neural network (GNN) models with loss functions derived from the probabilistic method to learn these probability distributions. We have evaluated our approach by its applications to two NP-hard problems: the (minimum) dominating-clique problem and the edge-clique-cover problem. Compared with the state-of-the-art solvers for both problems, our solver framework outputs competitive results. Specifically, for the (minimum) dominating-clique problem, our approach generates fewer branches than the solver presented by Culberson et al. (2005). For the edge-clique-cover problem, our approach produces smaller-sized edge clique covers (ECCs) than the solvers referenced by Conte et al. (2020) and Kellerman (1973).

Single-cell clustering is an important part of analyzing single-cell RNA-sequencing data. However, the accuracy and robustness of existing methods are disturbed by noise. One promising approach for addressing this challenge is integrating pathway information, which can alleviate noise and improve performance. In this work, we studied the impact on accuracy and robustness of existing single-cell clustering methods by integrating pathways. We collected 10 state-of-the-art single-cell clustering methods, 26 scRNA-seq datasets and four pathway databases, combined the AUCell method and the similarity network fusion to integrate pathway data and scRNA-seq data, and introduced three accuracy indicators, three noise generation strategies and robustness indicators. Experiments on this framework showed that integrating pathways can significantly improve the accuracy and robustness of most single-cell clustering methods.

MOTIVATION: CTCF-mediated chromatin loops underlie the formation of topological associating domains and serve as the structural basis for transcriptional regulation. However, the formation mechanism of these loops remains unclear, and the genome-wide mapping of these loops is costly and difficult. Motivated by the recent studies on the formation mechanism of CTCF-mediated loops, we studied the possibility of making use of transitivity-related information of interacting CTCF anchors to predict CTCF loops computationally. In this context, transitivity arises when two CTCF anchors interact with the same third anchor by the loop extrusion mechanism and bring themselves close to each other spatially to form an indirect loop. RESULTS: To determine whether transitivity is informative for predicting CTCF loops and to obtain an accurate and low-cost predicting method, we proposed a two-stage random-forest-based machine learning method, CTCF-mediated Chromatin Interaction Prediction (CCIP), to predict CTCF-mediated chromatin loops. Our two-stage learning approach makes it possible for us to train a prediction model by taking advantage of transitivity-related information as well as functional genome data and genomic data. Experimental studies showed that our method predicts CTCF-mediated loops more accurately than other methods and that transitivity, when used as a properly defined attribute, is informative for predicting CTCF loops. Furthermore, we found that transitivity explains the formation of tandem CTCF loops and facilitates enhancer-promoter interactions. Our work contributes to the understanding of the formation mechanism and function of CTCF-mediated chromatin loops. AVAILABILITY AND IMPLEMENTATION: The source code of CCIP can be accessed at: https://github.com/GaoLabXDU/CCIP. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Computational integrative analysis has become a significant approach in the data-driven exploration of biological problems. Many integration methods for cancer subtyping have been proposed, but evaluating these methods has become a complicated problem due to the lack of gold standards. Moreover, questions of practical importance remain to be addressed regarding the impact of selecting appropriate data types and combinations on the performance of integrative studies. Here, we constructed three classes of benchmarking datasets of nine cancers in TCGA by considering all the eleven combinations of four multi-omics data types. Using these datasets, we conducted a comprehensive evaluation of ten representative integration methods for cancer subtyping in terms of accuracy measured by combining both clustering accuracy and clinical significance, robustness, and computational efficiency. We subsequently investigated the influence of different omics data on cancer subtyping and the effectiveness of their combinations. Refuting the widely held intuition that incorporating more types of omics data always produces better results, our analyses showed that there are situations where integrating more omics data negatively impacts the performance of integration methods. Our analyses also suggested several effective combinations for most cancers under our studies, which may be of particular interest to researchers in omics data analysis.

We propose and study, theoretically and empirically, a new random model for the abstract argumentation framework (AF). Our model overcomes some intrinsic difficulties of the only random model of directed graphs in the literature that is relevant to AFs, and makes it possible to study the typical-case complexity of AF instances in terms of threshold behaviours and phase transitions. We proved that the probability for a random AF instance to have a stable/preferred extension goes through a sudden change (from 1 to 0) at the threshold of the parameters of the new model D(n, p, q), satisfying the equation 4q/((1 + q)(1+q)) = p. We showed, empirically, that in this new model, there is a clear easy-hard-easy pattern of hardness (for a typical backtracking-style exact solvers) associated with the phase transition. Our empirical studies indicated that instances from the new model at phase transitions are much harder than those from an Erdos-Renyi-style model with equal edge density. In addition to being an analytically tractable model for understanding the interplay between problems structures and effectiveness of (branching) heuristics used in practical argumentation solvers, the model can also be used to generate, in a systematic way, non-trivial AF instances with controlled features to evaluate the performance of other AF solvers.

Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order structure of a network. Higher-order structures such as the edge embeddedness and the size of communities may play more important roles in many online social networks. In this paper, we provide empirical evidence on the existence of rich higher-order structural characteristics in online social networks, develop mathematical models to interpret and model these characteristics, and discuss their various applications in practice. In particular, 1) We show that the embeddedness distribution of links in social networks has interesting and rich behavior that cannot be captured by well-known network models. 2) We formally prove that random k-tree, a recent model for complex networks, has a power law embeddedness distribution, and show empirically that the random k-tree model can be used to capture the rich behavior of higher-order structures we observed in real-world social network. 3) Going beyond the embeddedness, we show that a variant of the random k-tree model can be used to capture the power law distribution of the size of communities of overlapping cliques discovered recently.

In wireless sensor networks, we usually need to detect interesting events based on the information gathered from multiple sensors. One useful detection is to test whether or not the average sensory value within an area is larger than a given threshold. Such type of query is called geo-range query. It should report the geographic centers where the average value of nearby sensors is greater than a certain threshold. Answering geo-range query is nontrivial because we do not know in advance the satisfying geographic centers, which may not be necessarily the same as the locations of sensors. We develop two efficient algorithms: the brute-force search algorithm and the sweep-line algorithm. The brute-force search algorithm uses exhaustive search to enumerate all possible satisfying sub-regions. Its time complexity is O(n3), where n is the number of sensor nodes. The sweep-line algorithm uses a virtual line sweeping top-down through the plane. The algorithm takes O(n2log n) running time, and still obtains exact solution to the problem.

A general technique based on scoring scheme reweighting is proposed that can be used to speed up dynamic programming algorithms for a variety of pairwise sequence alignment problems. For the standard sequence alignment problem with an arbitrary gap penalty function, we show that a reweighted scoring scheme can be obtained by an efficient preprocessing step that computes a set of upper bounds on the score of the optimal alignment between pairs of suffixes of the sequences. A series of experiments on synthetic sequences and biological sequences indicate that our algorithm offers significant and robust speedup over the standard cubic-time dynamic programming algorithm. For sequences of length up to 2000 used in our experiments, the speedup factor ranges from 4 to more than 50. With a strong upper bound, a sub-cubic behavior in running time is also observed for all the tested situations.

In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to improve the efficiency of CSP algorithms, is in fact the key to the design of random CSP models that have interesting phase transition behavior and guaranteed exponential resolution complexity without putting much restriction on the parameter of constraint tightness or the domain size of the problem. We propose a very flexible framework for constructing problem instances withinteresting behavior and develop a variety of concrete methods to construct specific random CSP models that enforce different levels of constraint consistency. A series of experimental studies with interesting observations are carried out to illustrate the effectiveness of introducing structural elements in random instances, to verify the robustness of our proposal, and to investigate features of some specific models based on our framework that are highly related to the behavior of backtracking search algorithms.

In this paper, we investigate the space complexity of the Estimation of Distribution Algorithms (EDAs), a class of sampling-based variants of the genetic algorithm. By analyzing the nature of EDAs, we identify criteria that characterize the space complexity of two typical implementation schemes of EDAs, the factorized distribution algorithm and Bayesian network-based algorithms. Using random additive functions as the prototype, we prove that the space complexity of the factorized distribution algorithm and Bayesian network-based algorithms is exponential in the problem size even if the optimization problem has a very sparse interaction structure.

In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity. For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially. This, together with our empirical study for random instances generated below and in the phase transition region, suggests that the phase transition of the fixed ratio model is also easy.