UC Riverside researchers propose Pkd tree (parallel kd tree): a parallel kd tree that is efficient in both theory and practice

The exponential growth of multidimensional data in various fields, such as machine learning, geospatial analysis, and clustering, has posed significant challenges to traditional data structures. One such structure, the kd-tree, has long been a fundamental tool for managing high-dimensional data sets, supporting queries such as nearest neighbors, range searches, and clustering analysis. However, rapidly increasing data sizes are pushing the limits of current kd-tree implementations, which are struggling to keep up in terms of build time, scalability, and update efficiency, especially in parallel computing environments. Existing solutions are static, lack support for upgrades, or have poor scalability with today's large data sets. This gap between widespread use and the need for efficiency in construction, updates, and queries underscores the challenges of leveraging kd trees for high-performance applications.

The Pkd tree: an innovative solution

UC Riverside researchers propose the Pkd-tree (Parallel kd-tree), an innovative data structure that aims to address these challenges by introducing efficient parallelism in both theory and practice. The Pkd tree is designed for memory-efficient operations, supporting parallel construction, batch updates, and a variety of query types. This new approach enables significant improvements in handling large-scale multidimensional data compared to existing kd-tree variants. The core of the Pkd tree is based on novel algorithms that ensure optimal work complexity, high parallelism, and efficient cache usage. Through a combination of advanced construction techniques and careful engineering, researchers have created a kd tree that not only remains theoretically sound but also high-performing in practical environments.

Technical fundamentals and benefits

The technical foundations of the Pkd tree involve optimizing several key aspects of the kd tree construction and updating mechanisms. The researchers devised a parallel construction algorithm that simultaneously minimizes the work, span (representing the depth of parallel computation), and cache complexity. By determining the splitting hyperplane through a sophisticated sampling scheme and using a sieving mechanism to split points into subspaces with minimal data movement, they ensure that the Pkd tree remains balanced and optimized. Additionally, a rebuild-based update process helps keep the tree weight balanced without the need for full rebuilds after each modification. This approach produces a kd-tree structure that is not only efficient to construct but is also highly adaptable to dynamic data sets, allowing for fast insertion and deletion operations while maintaining the quality of query responses. Testing on synthetic and real-world data sets confirmed that the Pkd tree outperforms state-of-the-art parallel kd trees, delivering faster build and update times while maintaining or improving query efficiency.

Practical impact and results

The importance of the Pkd tree lies in its ability to address practical limitations that have long hindered the scalability of kd trees in parallel environments. In tests with well-established implementations such as CGAL and ParGeo, the Pkd tree consistently demonstrated superior performance. For example, when handling a data set of one billion points in two dimensions, the Pkd tree built the structure approximately 8 to 12 times faster than its closest competitors. Batch inserts and deletes were also significantly faster, showing up to a 40x speedup over existing methods like ParGeo's Log-tree. These improvements are largely due to the PKD tree's novel use of weight balancing, which avoids the need for inefficient rebuilds of the entire tree during updates, and its cache-efficient design, which ensures minimal data transfer during construction and the updates. The performance improvements of the Pkd tree are particularly evident in environments that require frequent modifications, making it a valuable tool for large-scale dynamic applications.

Conclusion

In conclusion, the PKD tree represents a significant advance in the field of data structures for multidimensional data management. By combining theoretical efficiency with practical performance, it bridges the gap between the need for high-speed, large-scale data management and the limitations of traditional kd-tree implementations. The Pkd tree's ability to efficiently support both dynamic construction and updates, along with optimized query performance, makes it an ideal candidate for applications ranging from spatial databases to real-time machine learning pipelines. UC Riverside research has therefore contributed a powerful new tool for data scientists and engineers working with massive data sets, allowing them to leverage kd trees more effectively and efficiently in both parallel and dynamic environments.

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