During the last decade GPU technology has shifted from pure general purpose computation to the inclusion of application specific integrated circuits (ASICs), such as Tensor Cores and Ray Tracing (RT) cores. Although these special purpose GPU cores were designed to further accelerate specific fields such as AI and real-time rendering, recent research has managed to exploit them to further accelerate other tasks that typically used regular GPU computing. In this work we present RTXRMQ, a new approach that can compute range minimum queries (RMQs) with RT cores. The main contribution is the proposal of a geometric solution for RMQ, where elements become triangles that are placed and shaped according to the element's value and position in the array, respectively, such that the closest hit of a ray launched from a point given by the query parameters corresponds to the result of that query. Experimental results show that RTXRMQ is currently best suited for small query ranges relative to the problem size, achieving up to $5\times$ and $2.3\times$ of speedup over state of the art CPU (HRMQ) and GPU (LCA) approaches, respectively. Although for medium and large query ranges RTXRMQ is currently surpassed by LCA, it is still competitive by being $2.5\times$ and $4\times$ faster than HRMQ which is a highly parallel CPU approach. Furthermore, performance scaling experiments across the latest RTX GPU architectures show that if the current RT scaling trend continues, then RTXRMQ's performance would scale at a higher rate than HRMQ and LCA, making the approach even more relevant for future high performance applications that employ batches of RMQs.

Accelerating Range Minimum Queries with Ray Tracing Cores

The Euler tour technique is a classical tool for designing parallel graph algorithms, originally proposed for the PRAM model. We ask whether it can be adapted to run efficiently on GPU. We focus on two established applications of the technique: (1) the problem of finding lowest common ancestors (LCA) of pairs of nodes in trees, and (2) the problem of finding bridges in undirected graphs. In our experiments, we compare theoretically optimal algorithms using the Euler tour technique against simpler heuristics supposed to perform particularly well on typical instances. We show that the Euler tour-based algorithms not only fulfill their theoretical promises and outperform practical heuristics on hard instances, but also perform on par with them on easy instances.

Adrian Siwiec

Papers

Euler Meets GPU: Practical Graph Algorithms with Theoretical Guarantees