This paper proposes efficient solutions for k -core decomposition with high parallelism. The problem of k -core decomposition is fundamental in graph analysis and has applications across various domains. However, existing algorithms face significant challenges in achieving work-efficiency in theory and/or high parallelism in practice, and suffer from various performance bottlenecks. We present a simple, work-efficient parallel framework for k -core decomposition that is easy to implement and adaptable to various strategies for improving work-efficiency. We introduce two techniques to enhance parallelism: a sampling scheme to reduce contention on high-degree vertices, and vertical granularity control (VGC) to mitigate scheduling overhead for low-degree vertices. Furthermore, we design a hierarchical bucket structure to optimize performance for graphs with high coreness values. We evaluate our algorithm on a diverse set of real-world and synthetic graphs. Compared to state-of-the-art parallel algorithms, including ParK, PKC, and Julienne, our approach demonstrates superior performance on 23 out of 25 graphs when tested on a 96-core machine. Our algorithm shows speedups of up to 315× over ParK, 33.4× over PKC, and 52.5× over Julienne.

The kd-tree is one of the most widely used data structures to manage multi-dimensional data. Due to the ever-growing data volume, it is imperative to consider parallelism in kd-trees. However, we observed challenges in existing parallel kd-tree implementations, for both constructions and updates. The goal of this paper is to develop efficient in-memory kd-trees by supporting high parallelism and cache-efficiency. We propose the Pkd-tree (Parallel kd-tree), a parallel kd-tree that is efficient both in theory and in practice. The Pkd-tree supports parallel tree construction, batch update (insertion and deletion), and various queries including k -nearest neighbor search, range query, and range count. We proved that our algorithms have strong theoretical bounds in work (sequential time complexity), span (parallelism), and cache complexity. Our key techniques include 1) an efficient construction algorithm that optimizes work, span, and cache complexity simultaneously, and 2) reconstruction-based update algorithms that guarantee the tree to be weight-balanced. With the new algorithmic insights and careful engineering effort, we achieved a highly optimized implementation of the Pkd-tree. We tested Pkd-tree with various synthetic and real-world datasets, including both uniform and highly skewed data. We compare the Pkd-tree with state-of-the-art parallel kd-tree implementations. In all tests, with better or competitive query performance, Pkd-tree is much faster in construction and updates consistently than all baselines. We released our code.

Computing strongly connected components (SCC) is among the most fundamental problems in graph analytics. Given the large size of today's real-world graphs, parallel SCC implementation is increasingly important. SCC is challenging in the parallel setting and is particularly hard on large-diameter graphs. Many existing parallel SCC implementations can be even slower than Tarjan's sequential algorithm on large-diameter graphs. To tackle this challenge, we propose an efficient parallel SCC implementation using a new parallel reachability approach. Our solution is based on a novel idea referred to as vertical granularity control (VGC). It breaks the synchronization barriers to increase parallelism and hide scheduling overhead. To use VGC in our SCC algorithm, we also design an efficient data structure called the parallel hash bag. It uses parallel dynamic resizing to avoid redundant work in maintaining frontiers (vertices processed in a round). We implement the parallel SCC algorithm by Blelloch et al. (J. ACM, 2020) using our new parallel reachability approach. We compare our implementation to the state-of-the-art systems, including GBBS, iSpan, Multi-step, and our highly optimized Tarjan's (sequential) algorithm, on 18 graphs, including social, web, k-NN, and lattice graphs. On a machine with 96 cores, our implementation is the fastest on 16 out of 18 graphs. On average (geometric means) over all graphs, our SCC is 6.0× faster than the best previous parallel code (GBBS), 12.8× faster than Tarjan's sequential algorithms, and 2.7× faster than the best existing implementation on each graph. We believe that our techniques are of independent interest. We also apply our parallel hash bag and VGC scheme to other graph problems, including connectivity and least-element lists (LE-lists). Our implementations improve the performance of the state-of-the-art parallel implementations for these two problems.

Influence Maximization (IM) is a crucial problem in data science. The goal is to find a fixed-size set of highly influentialseedvertices on a network to maximize the influence spread along the edges. While IM is NP-hard on commonly used diffusion models, a greedy algorithm can achieve (1 - 1/e)-approximation by repeatedly selecting the vertex with the highestmarginal gainin influence as the seed. However, we observe two performance issues in the existing work that prevent them from scaling to today's large-scale graphs: space-inefficient memorization to estimate marginal gain, and time-inefficient seed selection process due to a lack of parallelism. This paper significantly improves the scalability of IM using two key techniques. The first is asketch-compressiontechnique for the independent cascading model on undirected graphs. It allows combining the simulation and sketching approaches to achieve a time-space tradeoff. The second technique includes new data structures for parallel seed selection. Using our new approaches, we implementedPaC-IM: Parallel and Compressed IM. We comparePaC-IMwith state-of-the-art parallel IM systems on a 96-core machine with 1.5TB memory.PaC-IMcan process the ClueWeb graph with 978M vertices and 75B edges in about 2 hours. On average, across all tested graphs, our uncompressed version is 5--18x faster and about 1.4x more space-efficient than existing parallel IM systems. Using compression further saves 3.8x space with only 70% overhead in time on average.

The Log-Structured Merge (LSM) Tree has become a popular storage scheme for modern NoSQL and New SQL database systems. The LSM-tree scheme achieves high write throughput by first buffering writes in memory, then flushing them to the disk with sequential I/O. LSM-tree is an out-of-place structure, so the key range of a level in the tree can overlap with those of other levels. This negatively impacts range query performance, as multiple levels have to be scanned. Note that range queries are fundamental operators for other types of queries such as joins or spatiotemporal queries. To improve the read performance of LSM-trees, this paper proposes the Bi-directional LSM-tree, which differs from the classical LSM-tree in that hot records can move to higher levels to improve the overall LSM organization and benefit future range queries. The Bi-directional LSM-tree reuses the work performed during range queries to selectively generate a special type of components, called sentinel components. Our experiments show that the Bi-directional LSM-tree can save more than 10% of disk I/O compared to a standard Leveled LSM-tree.

Modern data-driven applications require that databases support fast analytical queries while undergoing rapid updates---often referred to as Hybrid Transactional Analytical Processing (HTAP). Achieving fast queries and updates in a database management system (DBMS) is challenging since optimizations to improve analytical queries can cause overhead for updates. One solution is to use snapshot isolation (SI) for multi-version concurrency control (MVCC) to allow readers to make progress regardless of concurrent writers. In this paper, we propose the Parallel Binary Tree (P-Tree) index structure to achieve SI and MVCC for multicore in-memory HTAP DBMSs. At their core, P-Trees are based on pure (immutable) data structures that use path-copying for updates for fast multi-versioning. They support tree nesting to improve OLAP performance while still allowing for efficient updates. The data structure also enables parallel algorithms for bulk operations on indexes and their underlying tables. We evaluate P-Trees on OLTP and OLAP benchmarks, and compare them with state-of-the-art data structures and DBMSs. Our experiments show that P-Trees outperform many concurrent data structures for the YCSB workload, and is 4--9 x faster than existing DBMSs for analytical queries, while also achieving reasonable throughput for simultaneous transactional updates.

Social influence and influence diffusion has been widely studied in online social networks. However, most existing works on influence diffusion focus on static networks. In this paper, we study the problem of maximizing influence diffusion in a dynamic social network. Specifically, the network changes over time and the changes can be only observed by periodically probing some nodes for the update of their connections. Our goal then is to probe a subset of nodes in a social network so that the actual influence diffusion process in the network can be best uncovered with the probing nodes. We propose a novel algorithm to approximate the optimal solution. The algorithm, through probing a small portion of the network, minimizes the possible error between the observed network and the real network. We evaluate the proposed algorithm on both synthetic and real large networks. Experimental results show that our proposed algorithm achieves a better performance than several alternative algorithms.