A systematic technique to bound factor-revealing linear programs is presented. We show how to derive a family of upper bound factor-revealing programs (UPFRP), and show that each such program can be solved by a computer to bound the approximation factor of an associated algorithm. Obtaining an UPFRP is straightforward, and can be used as an alternative to analytical proofs, that are usually very long and tedious. We apply this technique to the Metric Facility Location Problem (MFLP) and to a generalization where the distance function is a squared metric. We call this generalization the Squared Metric Facility Location Problem (SMFLP) and prove that there is no approximation factor better than 2.04, assuming P = NP. Then, we analyze the best known algorithms for the MFLP based on primal-dual and LP-rounding techniques when they are applied to the SMFLP. We prove very tight bounds for these algorithms, and show that the LP-rounding algorithm achieves a ratio of 2.04, and therefore has the best factor for the SMFLP. We use UPFRPs in the dual-fitting analysis of the primal-dual algorithms for both the SMFLP and the MFLP, improving some of the previous analysis for the MFLP.

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Network motif algorithms have been a topic of research mainly after the 2002-seminal paper from Milo et al. [1], which provided motifs as a way to uncover the basic building blocks of most networks. Motifs have been mainly applied in Bioinformatics, regarding gene regulation networks. Motif detection is based on induced subgraph counting. This paper proposes an algorithm to count subgraphs of size k + 2 based on the set of induced subgraphs of size k. The general technique was applied to detect 3, 4 and 5-sized motifs in directed graphs. Such algorithms have time complexity O(a(G)m), O(m(2)) and O(nm(2)), respectively, where a(G) is the arboricity of G(V, E). The computational experiments in public data sets show that the proposed technique was one order of magnitude faster than Kavosh and FANMOD. When compared to NetMODE, acc-Motif had a slightly improved performance.

With several good research groups actively working in machine learning (ML) approaches, we have now the concept of self-containing machine learning solutions that oftentimes work out-of-the-box leading to the concept of ML black-boxes. Although it is important to have such black-boxes helping researchers to deal with several problems nowadays, it comes with an inherent problem increasingly more evident: we have observed that researchers and students are progressively relying on ML black-boxes and, usually, achieving results without knowing the machinery of the classifiers. In this regard, this paper discusses the use of machine learning black-boxes and poses the question of how far we can get using these out-of-the-box solutions instead of going deeper into the machinery of the classifiers. The paper focuses on three aspects of classifiers: (1) the way they compare examples in the feature space; (2) the impact of using features with variable dimensionality; and (3) the impact of using binary classifiers to solve a multi-class problem. We show how knowledge about the classifier's machinery can improve the results way beyond out-of-the-box machine learning solutions.

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This paper presents an extension of the RMFinder technique, previously proposed to identify representative models (RMs) within the decision-making process in oil fields. As there are several uncertainties associated with this decision-making process, a large number of scenarios are supposed to be analyzed, so that high-quality production strategies can be defined. Such broad analysis is often unfeasible, so techniques to automatically identify RMs are particularly relevant. The original RMFinder does not consider the individual probability of each RM, which may not be accurate when the risk curves of the problem are estimated. Therefore, a mechanism to calculate the individual probability of each RM was developed here, together with a graphical way to visualize different proposals of RMs. To automatically identify the optimal probability of each RM, this new version of RMFinder minimizes the deviation between the risk curves generated with the selected RMs and the original risk curves of the problem. The graphical approach automatically exhibits, in a single page per solution, the RM dispersion in the scatter plots, the resulting risk curves and the differences between attribute-level distributions. This helps the decision makers to visualize and compare different sets of RMs. The proposed methodology was applied to a small synthetic problem and to three reservoir models based on real-world Brazilian fields: (i) UNISIM-I-D, a benchmark case based on the Namorado field; (ii) UNISIM-II-Dβ, a benchmark case based on a highly fractured pre-salt carbonate reservoir; and (iii) ST001a, a highly heterogeneous heavy oil offshore field. The obtained sets of RMs were evaluated by experts and considered appropriate to the studied problems, being adopted as the standard models in the following steps of the decision-making process to define the production strategies under uncertainties.

We consider the uniform metric labeling problem. This NP-hard problem considers how to assign objects to labels respecting assignment and separation costs. The known approximation algorithms are based on solutions of large linear programs and are impractical for moderate-and large-size instances. We present an 8 log n-approximation algorithm that can be applied to large-size instances. The algorithm is greedy and is analyzed by a primal-dual technique. We implemented the presented algorithm and two known approximation algorithms and compared them at randomized instances. The gain of time was considerable with small error ratios. We also show that the analysis is tight, up to a constant factor.