Breadth-first search (BFS) is a fundamental building block of various high-performance computing applications beyond graph analysis and also known as a benchmark problem in the Graph 500 list. The increasing volume of global data demands efficient distributed BFS, which, however, is hindered by the high communication costs of exchanging vertex data between compute nodes. To address this challenge, this paper introduces four techniques: (i) forest pruning, which reduces the number of vertices by eliminating those unnecessary for the search; (ii) group reordering and (iii) multilevel bitmap compression, which decrease the memory footprint of graph data, thereby enabling fewer nodes to manage larger graphs; and (iv) adaptive parameter tuning, which quickly optimizes the hyperparameters of the BFS algorithm. In the evaluation using 152,064 nodes of the supercomputer Fugaku, our implementation achieved 198 tera-traversed edges per second, doubling the performance reported in the latest Graph500-related study on Fugaku.

Graph embedding is the process of obtaining a vector representation of graph nodes. The representation obtained by graph embedding is highly versatile. It can be used for various tasks, such as recommendation and clustering tasks. However, there are only a few methods that incorporate attributes indicating node characteristics, such as user gender, age, or product category, into graph embedding. Therefore, we hypothesize that nodes with the same attribute are often connected to the same node. Consequently, we propose two methods for graph embedding, parallel and serial, that use metric learning to reflect attribute data in node features. The proposed method can be applied to any graph embedding and metric learning method, and thus can also be applied to many new methods yet to be developed. Numerical experimental results show that the proposed method using node attributes is superior to the existing methods in both AUROC and accuracy.

Deep learning models are vulnerable to adversarial examples, and adversarial attacks used to generate such examples have attracted considerable research interest. Although existing methods based on the steepest descent have achieved high attack success rates, ill-conditioned problems occasionally reduce their performance. To address this limitation, we utilize the conjugate gradient (CG) method, which is effective for this type of problem, and propose a novel attack algorithm inspired by the CG method, named the Auto Conjugate Gradient (ACG) attack. The results of large-scale evaluation experiments conducted on the latest robust models show that, for most models, ACG was able to find more adversarial examples with fewer iterations than the existing SOTA algorithm Auto-PGD (APGD). We investigated the difference in search performance between ACG and APGD in terms of diversification and intensification, and define a measure called Diversity Index (DI) to quantify the degree of diversity. From the analysis of the diversity using this index, we show that the more diverse search of the proposed method remarkably improves its attack success rate.

Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for post-quantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. CMAP-LAP facilitates the implementation of large-scale parallel strategies for lattice problems since all the functions are designed to be customizable and abstract. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments.