Graph embedding, which maps graph nodes to lowdimensional vectors, is a widely used technique for graph representation learning. However, most existing graph embedding models suffer from high memory consumption, limiting their scalability to large graphs. Heterogeneous memory systems that combine DRAM and Persistent Memory (PM) offer new opportunities for scaling up memory capacity. Despite this advantage, the performance gap (on the order of 5x) between DRAM and PM is magnified (by 3.3-4.2x) under non-uniform memory access (NUMA) architecture. Additionally, the inherent sparsity of graphs induces numerous random accesses in the fundamental Sparse Matrix and Dense Matrix Multiplication (SpMM) operations of graph embedding, hindering high-performance heterogeneous memory processing. To address these challenges, this paper presents OMeGa that focuses on Optimizing heterogeneous Memory processing for large-scale Graph embedding. OMeGa leverages an entropy-aware thread allocation, simultaneously achieving workload balancing and tail latency reduction across threads. It also incorporates a workload feature-aware prefetcher to alleviate random accesses during streaming heterogeneous processing. In addition, OMeGa devises a NUMA-aware data placement, aiming to minimize the adverse impact of NUMA on heterogeneous memory. The experiments conducted on billion-scale graphs demonstrate that OMeGa exhibits an average acceleration of 32.03x with strong scalability. This pioneering capability enables the efficient generation of large-scale graph embeddings, free from the memory size constraints and performance disparities typically encountered in heterogeneous memory systems.

The learned index technique has been widely explored as a strong competitor to traditional indexes. It adopts static learning-based models to fit the distribution of sorted data and locate keys through predictions, which shows outstanding query speed. However, frequent retraining is required when it comes to concurrent insertion scenarios. Despite existing studies introducing sparse slots and delta buffers to mitigate this effect, the read-write performance of the learned index still falls short of expectations, especially in concurrent conditions. In this paper, we first propose a novel hybrid index scheme that combines a read-efficient learned index with an insert-efficient Adaptive Radix Tree (ART) to realize high performance for read-write scenarios. However, it is not trivial due to expensive model prediction errors, complicated model hierarchy, and redundant node traversals. Therefore, we then introduce ALT-index, an efficient hybrid learned index with high concurrency for memory database systems. ALT-index highlights a delicate two-tier architecture where linear data are stored in the learned index without prediction errors and conflict data are hosted in the lower layer as an optimized ART. Besides, we develop a Greedy Pessimistic Linear (GPL) algorithm to support flattened data structures for concurrency. In the optimized ART layer, we introduce a fast and compact pointer buffer to further improve the overall performance. Experimental results conducted on various real-world datasets with 32 threads illustrate that ALT-index improves performance by up to 1.9x, 2.1x, and 2.3x compared with ALEX+, FINEdex, and XIndex in read-write-balanced scenarios, respectively.

Graph embedding maps graph nodes to low-dimensional vectors and is widely used in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on Twitter with over one billion edges. Most existing graph embedding methods fall short of reaching high data scalability. In this paper, we present a general-purpose, distributed, information-centric random walk-based, and pipeline-optimized graph embedding framework,$\sf{DistGER-Pipe}$DistGER−Pipe, which scales to embed billion-edge graphs.$\sf{DistGER-Pipe}$DistGER−Pipeincrementally computes information-centric random walks to reduce redundant computations for more effective and efficient graph embedding. It further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines.$\sf{DistGER-Pipe}$DistGER−Pipealso improves the distributed$\sf{Skip-Gram}$Skip−Gramlearning model to generate node embeddings by optimizing access locality, CPU throughput, and synchronization efficiency. Finally,$\sf{DistGER-Pipe}$DistGER−Pipedesigns pipelined execution that decouples the operators in sampling and training procedures with an inter-round serial and intra-round parallel processing, attaining optimal utilization of computing resources. Experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including$\sf{KnightKing}$KnightKing,$\sf{DistDGL}$DistDGL,$\sf{Pytorch-BigGraph}$Pytorch−BigGraph, and$\sf{DistGER}$DistGER,$\sf{DistGER-Pipe}$DistGER−Pipeexhibits 3.15×–1053× acceleration, 45% reduction in cross-machines communication, >10% effectiveness improvement in downstream tasks, and 38% enhancement in CPU utilization.

Key- Value Stores (KVS) implemented with log- structured merge-tree (LSM-tree) have gained widespread ac-ceptance in storage systems. Nonetheless, a significant challenge arises in the form of high write amplification due to the compaction process. While KV-separated LSM-trees successfully tackle this issue, they also bring about substantial space am-plification problems, a concern that cannot be overlooked in cost-sensitive scenarios. Garbage collection (GC) holds significant promise for space amplification reduction, yet existing GC strategies often fall short in optimization performance, lacking thorough consideration of workload characteristics. Additionally, current KV-separated LSM-trees also ignore the adverse effect of the space amplification in the index LSM-tree. In this paper, we systematically analyze the sources of space amplification of KV- separated LSM-trees and introduce Scavenger, which achieves a better trade-off between performance and space amplification. Scavenger initially proposes an I/O-efficient garbage collection scheme to reduce I/O overhead and incorporates a space-aware compaction strategy based on compensated size to minimize the space amplification of index LSM-trees. Extensive experiments show that Scavenger significantly improves write performance and achieves lower space amplification than other KV-separated LSM-trees (including BlobDB, Titan, and TerarkDB).

Graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on Twitter with over one billion edges. Most existing graph embedding methods fall short of reaching high data scalability. In this paper, we present a general-purpose, distributed, information-centric random walk-based graph embedding framework, DistGER, which can scale to embed billion-edge graphs. DistGER incrementally computes information-centric random walks. It further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines. DistGER also improves the distributed Skip-Gram learning model to generate node embeddings by optimizing the access locality, CPU throughput, and synchronization efficiency. Experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including KnightKing, DistDGL, and Pytorch-BigGraph, DistGER exhibits 2.33×--129× acceleration, 45% reduction in cross-machines communication, and >10% effectiveness improvement in downstream tasks.

Graph embedding is becoming widely adopted as an efficient way to learn graph representations required to solve graph analytics problems. However, most existing graph embedding methods, owing to computation-efficiency challenges for large-scale graphs, generally employ a one-size-fits-all strategy to extract information, resulting in a large amount of redundant or inaccurate representations. In this work, we propose HuGE, an efficient and scalable graph embedding method enabled by an entropy-driven mechanism. Specifically, HuGE leverages hybrid-property heuristic random walk to capture node features, which considers both node degree and the number of common neighbors in each walking step. More importantly, to guarantee information effectiveness of sampling, HuGE adopts two heuristic methods to decide the random walk length and the number of walks per node, respectively. Extensive experiments on real-world graphs demonstrate that HuGE achieves both efficiency and performance advantages over recent popular graph embedding approaches. For link prediction and multi-label classification, our approach not only offers >10% average gains, but also exhibits 22×-126× speedup compared with existing sampling-based methods.

Reservoir sampling is widely employed to characterize connectivity of large graph streams by producing edge samples. However, existing reservoir-based sampling methods mainly characterize large graph streams by a measure of counting triangles but perform poorly in accuracy when used to analyze the topological characteristics reflected by node degrees because they produce disconnected edge samples, making them ineffective in many applications that require both types of connectivity estimation simultaneously in real time. This paper proposes a new method, called triangle-induced reservoir sampling, or T-Sample, to produce connected edge samples. While every edge in a graph stream is still processed only once by T-Sample, a dual sampling mechanism performing both uniform sampling and non-uniform sampling is carefully designed with a base reservoir and an incremental reservoir. Specifically, the uniform sampling can be used to count triangles by employing the existing algorithms while the non-uniform sampling ensures that the edge samples are connected. Experimental results driven by real datasets show that T-Sample can obtain much more accurate estimations on the distributions of node degrees than the existing reservoir-based sampling methods.