This paper presents two new bidirectional heuristic search algorithms for solving the shortest path problem on graphs: consistent-heuristic bucket-based bidirectional search (CBBS) and front-to-front GPU bidirectional search (FFGBS). CBBS uses a consistent heuristic and groups nodes into buckets that organize nodes based on estimated path cost and known heuristic errors. FFGBS splits the work between the CPU and GPU, with the GPU solving a front-to-front heuristic and the CPU choosing nodes to expand. This paper also includes a new front-to-front version of the GAP heuristic for the pancake problem that is efficient to solve on a GPU. Computational experiments for CBBS are performed on the pancake problem. CBBS is faster and requires less node expansions with the GAP-1 heuristic, compared to bidirectional state of the algorithms like DIBBS and DVCBS. Computational experiments for FFGBS are performed on the pancake problem and DIMACS road network, showing that FFGBS is consistently the fastest algorithm on all but the smallest pancake stacks when using the GAP-2 heuristic and is also the fastest algorithm on the largest road networks.

本文提出了两种新的双向启发式搜索算法，用于解决图上的最短路径问题：一致启发式基于桶的双向搜索 (CBBS) 和前端到前端 GPU 双向搜索 (FFGBS)。CBBS 使用一致的启发式方法并将节点分组到桶中，这些桶根据估计的路径成本和已知的启发式错误来组织节点。FFGBS 在 CPU 和 GPU 之间拆分工作，GPU 解决从前到前的启发式算法，CPU 选择要扩展的节点。本文还包括一个新的前端到前端版本的 GAP 启发式方法，用于在 GPU 上高效解决煎饼问题。CBBS 的计算实验是在煎饼问题上进行的。CBBS 更快，并且使用 GAP-1 启发式算法需要更少的节点扩展，与 DIBBS 和 DVCBS 等算法的双向状态相比。FFGBS 的计算实验在 pancake 问题和 DIMACS 道路网络上进行，表明当使用 GAP-2 启发式算法时，FFGBS 始终是除最小 pancake 堆栈之外的所有其他算法中最快的算法，并且也是最大道路网络上最快的算法。