Several NP-hard problems are solved exactly using exponential-time branching strategies, whether it be branch-and-bound algorithms, or bounded search trees in fixed-parameter algorithms. The number of tractable instances that can be handled by sequential algorithms is usually small, whereas massive parallelization has been shown to significantly increase the space of instances that can be solved exactly. However, previous centralized approaches require too much communication to be efficient, whereas decentralized approaches are more efficient but have difficulty keeping track of the global state of the exploration. In this work, we propose to revisit the centralized paradigm while avoiding previous bottlenecks. In our strategy, the center has lightweight responsibilities, requires only a few bits for every communication, but is still able to keep track of the progress of every worker. In particular, the center never holds any task but is able to guarantee that a process with no work always receives the highest priority task globally. Our strategy was implemented in a generic C++ library called GemPBA, which allows a programmer to convert a sequential branching algorithm into a parallel version by changing only a few lines of code. An experimental case study on the vertex cover problem demonstrates that some of the toughest instances from the DIMACS challenge graphs that would take months to solve sequentially can be handled within two hours with our approach.

翻译：若干NP难问题通过指数时间分支策略精确求解，包括分支定界算法和固定参数算法中的有界搜索树。串行算法可处理的可解实例数量通常有限，而大规模并行化已被证明能显著扩展可精确求解的实例空间。然而，现有集中式方法因通信开销过大而效率低下，分布式方法虽更高效却难以跟踪全局探索状态。本文提出在规避传统瓶颈的同时重新审视集中式范式。在该策略中，中心节点承担轻量级职责，每次通信仅需若干比特，仍能跟踪各工作节点的进度。特别地，中心节点无需持有任何任务，但可确保空闲进程始终获得全局优先级最高的任务。该策略已在通用C++库GemPBA中实现，程序员仅需修改少量代码即可将串行分支算法转换为并行版本。针对顶点覆盖问题的实验案例研究表明，DIMACS挑战图中需数月串行求解的最难实例，采用本方法可在两小时内完成处理。