GPU‐accelerated backtracking using CUDA Dynamic Parallelism

Abstract

Summary New GPGPU technologies, such as CUDA Dynamic Parallelism (CDP), can help dealing with recursive patterns of computation, such as divide‐and‐conquer, used by backtracking algorithms. In this paper, we propose a GPU‐accelerated backtracking algorithm using CDP that extends a well‐known parallel backtracking model. The search starts on CPU, processing the search tree until a first cutoff depth. Based on this partial backtracking tree, the algorithm analyzes the memory requirements of subsequent kernel generations. The proposed algorithm performs no dynamic allocation of memory on GPU, unlike related works from the literature. The proposed algorithm has been extensively tested using the N‐Queens Puzzle problem and instances of the Asymmetric Traveling Salesman Problem (ATSP) as test‐cases. The proposed CDP algorithm may, under some conditions, outperform its non‐CDP counterpart by a factor up to 25. But, it may also be up to twice slower. The CDP‐based implementation has much better worst case execution times and makes algorithm's performance less dependent on the tuning of parameters. Compared to other CDP‐based strategies from the literature, the proposed algorithm is on average 8× faster. The proposed algorithm is also hybridized with another CDP‐based strategy from the literature. The combination of strategies is in average 4.5× faster than the related strategy. We also identify some difficulties, limitations, and bottlenecks concerning the CDP programming model which may be useful for helping potential users.

Productivity-Aware Design and Implementation of Distributed Tree-Based Search Algorithms

“…As these algorithms are compute-intensive, diverse strategies have been used for improving performance, such as instruction-level parallelism, architecturespecific code optimizations and problem-specific data structures [6,12,14,17]. Thus, parallel tree-based search algorithms are frequently written in C/C++, due to their low-level features and supported parallel computing libraries [5].…”

“…The N-Queens problem consists in placing N non-attacking queens on a N ×N chessboard, and it is often used as a benchmark for novel tree-based search algorithms [3,12]. The N-Queens is easily modeled as a permutation problem: position r of a permutation of size N designates the column in which a queen is placed in row r. Furthermore, the concepts herein presented are similar to any permutation combinatorial problem and can be adapted for solving other problems of this class with straightforward modifications [6,14].…”

“…The kernel of both parallel algorithms previously presented is based on a serial and hand optimized backtracking for solving permutation combinatorial problems, originally written in C [6]. The serial backtracking was then adapted to Chapel, obeying the handmade optimizations, instruction-level parallelism, data structures, and C-types.…”

“…Tree-based search algorithms are compute-intensive and highly irregular, which demands hand-optimized data structures for efficient search and load balancing [6,14,17]. Thus, high-productivity languages are not often employed within the scope of tree search, as they historically suffer from severe performance penalties [11].…”

HPC & Co strike back: Where are distributed paradigms heading toward?

“…Other two papers describe algorithms that tend to optimize the use of modern architectures in the context of specific applications. Carneiro Pessoa et al 78 presented an algorithm to exploit GPUs for backtracking search algorithms, ie, irregular algorithms that need an unpredictable number of computations and an unknown degree of parallelism. This algorithm relies on CUDA dynamic parallelism and a method to avoid dynamic memory allocation on GPU.…”