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Bayesian optimization algorithms are widely used for solving problems with a high computational complexity in terms of objective function evaluation. The efficiency of Bayesian optimization is strongly dependent on the quality of the surrogate models of an objective function, which are built and refined at each iteration. The quality of surrogate models, and hence the performance of an optimization algorithm, can be greatly improved by selecting the appropriate hyperparameter values of the approximation algorithm. The common approach to finding good hyperparameter values for each iteration of Bayesian optimization is to build surrogate models with different hyperparameter values and choose the best one based on some estimation of the approximation error, for example, a cross-validation score. Building multiple surrogate models for each iteration of Bayesian optimization is computationally demanding and significantly increases the time required to solve an optimization problem. This paper suggests a new approach, called exploratory landscape validation, to find good hyperparameter values with less computational effort. Exploratory landscape validation metrics can be used to predict the best hyperparameter values, which can improve both the quality of the solutions found by Bayesian optimization and the time needed to solve problems. [ABSTRACT FROM AUTHOR]

Conceptual distance refers to the degree of proximity between two concepts within a conceptualization. It is closely related to semantic similarity and relationships, but its measurement strongly depends on the context of the given concepts. DIS-C represents an advancement in the computation of semantic similarity/relationships that is independent of the type of knowledge structure and semantic relations when generating a graph from a knowledge base (ontologies, semantic networks, and hierarchies, among others). This approach determines the semantic similarity between two indirectly connected concepts in an ontology by propagating local distances by applying an algorithm based on the All Pairs Shortest Path (APSP) problem. This process is implemented for each pair of concepts to establish the most effective and efficient paths to connect these concepts. The algorithm identifies the shortest path between concepts, which allows for an inference of the most relevant relationships between them. However, one of the critical issues with this process is computational complexity, combined with the design of APSP algorithms, such as Dijkstra, which is n 3 . This paper studies different alternatives to improve the DIS-C approach by adapting approximation algorithms, focusing on Dijkstra, pruned Dijkstra, and sketch-based methods, to compute the conceptual distance according to the need to scale DIS-C to analyze very large graphs; therefore, reducing the related computational complexity is critical. Tests were performed using different datasets to calculate the conceptual distance when using the original version of DIS-C and when using the influence area of nodes. In situations where time optimization is necessary for generating results, using the original DIS-C model is not the optimal method. Therefore, we propose a simplified version of DIS-C to calculate conceptual distances based on centrality estimation. The obtained results for the simple version of DIS-C indicated that the processing time decreased 2.381 times when compared to the original DIS-C version. Additionally, for both versions of DIS-C (normal and simple), the APSP algorithm decreased the computational cost when using a two-hop coverage-based approach. [ABSTRACT FROM AUTHOR]

Connectivity has significance in both of data collection and aggregation for Wireless Sensor Networks (WSNs). Once the connectivity is lost, relay nodes are deployed to build a Steiner Minimal Tree (SMT) such that the inter-component connection is reestablished. In recent years, there has been a growing interest in connectivity restoration problems. In previous works, the deployment area of a WSN is assumed to be flat without obstacles. However, such an assumption is not realistic. In addition, most of the existing strategies chose the representative of each component, which serves as the starting point of relay node deployment during the connectivity restoration, either in a random way or in the shortest-distance based manner. In fact, both ways of representative selection could potentially increase the length of the SMT such that more relay nodes are required. In this paper, a novel connectivity restoration strategy is proposed--Obstacle-Avoid connectivity restoration strategy based on Straight Skeletons (OASS), which employs both the polygon based representative selection with the presence of obstacles and the straight skeleton based SMT establishment. The OASS is proved to be a 3-opt approximation algorithm with the complexity of O(n log n), and the approximation ratio can reduce to 3 p 3 2 while it satisfies a certain condition. The theoretical analysis and simulations show that the performance of the OASS is better than other strategies in terms of the relay count and the quality of the established topology (i.e., distances between components, delivery latency and balanced traffic load) as well. [ABSTRACT FROM AUTHOR]

This paper investigates resource optimization schemes in a marine communication scenario based on non-orthogonal multiple access (NOMA). According to the offshore environment of the South China Sea, we first establish a Longley–Rice-based channel model. Then, the weighted achievable rate (WAR) is considered as the optimization objective to weigh the information rate and user fairness effectively. Our work introduces an improved joint power and user allocation scheme (RBPUA) based on a single resource block. Taking RBPUA as a basic module, we propose three joint multi-subchannel power and marine user allocation algorithms. The gradient descent algorithm (GRAD) is used as the reference standard for WAR optimization. The multi-choice knapsack algorithm combined with dynamic programming (MCKP-DP) obtains a WAR optimization result almost equal to that of GRAD. These two NOMA-based solutions are able to improve WAR performance by 7.47% compared with OMA. Due to the high computational complexity of the MCKP-DP, we further propose a DP-based fully polynomial-time approximation algorithm (DP-FPTA). The simulation results show that DP-FPTA can reduce the complexity by 84.3% while achieving an approximate optimized performance of 99.55%. This advantage of realizing the trade-off between performance optimization and complexity meets the requirements of practical low-latency systems. [ABSTRACT FROM AUTHOR]

Proposed algorithms for calculating the shortest paths such as Dijikstra and Flowd-Warshall's algorithms are limited to small networks due to computational complexity and cost. We propose an efficient and a more accurate approximation algorithm that is applicable to large scale networks. Our algorithm iteratively constructs levels of hierarchical networks by a node condensing procedure to construct hierarchical graphs until threshold. The shortest paths between nodes in the original network are approximated by considering their corresponding shortest paths in the highest hierarchy. Experiments on real life data show that our algorithm records high efficiency and accuracy compared with other algorithms. [ABSTRACT FROM AUTHOR]

We consider the coordination of transportation and batching scheduling with one single vehicle for minimizing total weighted completion time. The computational complexity of the problem with batch capacity of at least 2 was posed as open in the literature. For this problem, we show the unary NP-hardness for every batch capacity at least 3 and present a polynomial-time 3-approximation algorithm when the batch capacity is at least 2. [ABSTRACT FROM AUTHOR]

Integrated information theory (IIT) proposes a measure of integrated information, termed Phi (Φ), to capture the level of consciousness of a physical system in a given state. Unfortunately, calculating Φ itself is currently possible only for very small model systems and far from computable for the kinds of system typically associated with consciousness (brains). Here, we considered several proposed heuristic measures and computational approximations, some of which can be applied to larger systems, and tested if they correlate well with Φ. While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT and, thus, whether they can be used to test the theory. In this study, we evaluated these approximations and heuristic measures considering how well they estimated the Φ values of model systems and not on the basis of practical or clinical considerations. To do this, we simulated networks consisting of 3–6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system's state transition probability matrix (TPM) and generated observed data over time from all possible initial conditions. We then calculated Φ, approximations to Φ, and measures based on state differentiation, coalition entropy, state uniqueness, and integrated information. Our findings suggest that Φ can be approximated closely in small binary systems by using one or more of the readily available approximations (r > 0.95) but without major reductions in computational demands. Furthermore, the maximum value of Φ across states (a state-independent quantity) correlated strongly with measures of signal complexity (LZ, rs = 0.722), decoder-based integrated information (Φ*, rs = 0.816), and state differentiation (D1, rs = 0.827). These measures could allow for the efficient estimation of a system's capacity for high Φ or function as accurate predictors of low- (but not high-)Φ systems. While it is uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ be, at a minimum, rigorously tested in an environment where the ground truth can be established. [ABSTRACT FROM AUTHOR]

This special issue of Algorithms is devoted to the design and analysis of algorithms for solving combinatorial problems of a theoretical or practical nature involving graphs, with a focus on computational complexity. [ABSTRACT FROM AUTHOR]