Let k denote an integer greater than 2, let G denote a k-partite graph, and let S denote the set of all maximal k-partite cliques in G. Several open questions concerning the computation of S are resolved. A straightforward and highly-scalable modification to the classic recursive backtracking approach of Bron and Kerbosch is first described and shown to run in O(3^n/3) time. A series of novel graph constructions is then used to prove that this bound is best possible in the sense that it matches an asymptotically tight upper limit on |S|. The task of identifying a vertex-maximum element of S is also considered and, in contrast with the k = 2 case, shown to be NP-hard for every k ≥ 3. A special class of k-partite graphs that arises in the context of functional genomics and other problem domains is studied as well and shown to be more readily solvable via a polynomial-time transformation to bipartite graphs. Applications, limitations, potentials for faster methods, heuristic approaches, and alternate formulations are also addressed.

Accurately predicting flight delays remains a significant challenge in the aviation industry due to the complexity and interconnectivity of its operations. The traditional prediction methods often rely on meteorological conditions, such as temperature, humidity, and dew point, as well as flight-specific data like departure and arrival times. However, these predictors frequently fail to capture the nuanced dynamics that lead to delays. This paper introduces network centrality measures as novel predictors to enhance the binary classification of flight arrival delays. Additionally, it emphasizes the use of tree-based ensemble models, specifically random forest, gradient boosting, and CatBoost, which are recognized for their superior ability to model complex relationships compared to single classifiers. Empirical testing shows that incorporating centrality measures improves the models’ average performance, with random forest being the most effective, achieving an accuracy rate of 86.2%, surpassing the baseline by 1.7%.

We present an algorithm to test whether a given graphical degree sequence is forcibly connected or not and prove its correctness. We also outline the extensions of the algorithm to test whether a given graphical degree sequence is forcibly $k$-connected or not for every fixed $k\ge 2$. We show through experimental evaluations that the algorithm is efficient on average, though its worst case run time is probably exponential. We also adapt Ruskey et al's classic algorithm to enumerate zero-free graphical degree sequences of length $n$ and Barnes and Savage's classic algorithm to enumerate graphical partitions of even integer $n$ by incorporating our testing algorithm into theirs and then obtain some enumerative results about forcibly connected graphical degree sequences of given length $n$ and forcibly connected graphical partitions of given even integer $n$. Based on these enumerative results we make some conjectures such as: when $n$ is large, (1) almost all zero-free graphical degree sequences of length $n$ are forcibly connected; (2) almost none of the graphical partitions of even $n$ are forcibly connected.

Naive Bayesian approach is an effective method for many data analysis problems such as pattern classification and machine learning. However, it often suffers from the underflow problem when the input data has a high dimension. Such a problem is often addressed by taking logarithms and working in the transformed domain. In this paper we propose a novel approach to this problem based on geometric means and apply it to the classical MNIST handwritten digit classification problem. The results show that it not only achieves satisfactory accuracy but also demonstrates its power of presenting "second best" guesses that are meaningful and useful in the pattern classification domain.