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Yayın Crossing minimization in weighted bipartite graphs(Elsevier B.V., 2009-12) Çakıroğlu, Olca Arda; Erten, Cesim; Karataş, Ömer; Sözdinler, MelihGiven a bipartite graph G = (L0, L1, E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 that minimizes the number of crossings has received much attention in literature. The problem is NP-complete in general and several practically efficient heuristics and polynomial-time algorithms with a constant approximation ratio have been suggested. We generalize the problem and consider the version where the edges have nonnegative weights. Although this problem is more general and finds specific applications in automatic graph layout problems similar to those of the unweighted case, it has not received as much attention. We provide a new technique that efficiently approximates a solution to this more general problem within a constant approximation ratio of 3. In addition we provide appropriate generalizations of some common heuristics usually employed for the unweighted case and compare their performances.Yayın ANN activation function estimators for homomorphic encrypted inference(Institute of Electrical and Electronics Engineers Inc., 2025-06-13) Harb, Mhd Raja Abou; Çeliktaş, BarışHomomorphic Encryption (HE) enables secure computations on encrypted data, facilitating machine learning inference in sensitive environments such as healthcare and finance. However, efficiently handling non-linear activation functions, specifically Sigmoid and Tanh, remains a significant computational challenge for encrypted inference using Artificial Neural Networks (ANNs). This study introduces a lightweight, ANN-based estimator designed to accurately approximate activation functions under homomorphic encryption. Unlike traditional polynomial and piecewise linear approximations, the proposed ANN estimators achieve superior accuracy with lower computational overhead associated with bootstrapping or high-degree polynomial techniques. These estimators are trained on plaintext data and seamlessly integrated into encrypted inference pipelines, significantly outperforming conventional methods. Experimental evaluations demonstrate notable improvements, with ANN estimators enhancing accuracy by approximately 2% for Sigmoid and up to 73% for Tanh functions, improving F1-scores by approximately 2% for Sigmoid and up to 88% for Tanh, and markedly reducing Mean Square Error (MSE) by up to 96% compared to polynomial approximations. The ANN estimator achieves an accuracy of 97.70% and an AUC of 0.9997 when integrated into a CNN architecture on the MNIST dataset, and an accuracy of 85.25% with an AUC of 0.9459 on the UCI Heart Disease dataset during ciphertext inference. These results underscore the estimator’s practical effectiveness and computational feasibility, making it suitable for secure and efficient ANN inference in encrypted environments.
