We present new refinement heuristics for the balanced graph partitioning problem that break with an age-old rule. Traditionally, local search only permits moves that keep the block sizes balanced (below a size constraint). In this work, we demonstrate that admitting large temporary balance violations drastically improves solution quality. The effects are particularly strong on irregular instances such as social networks. Designing efficient implementations of this general idea involves both careful selection of candidates for unconstrained moves as well as algorithms for rebalancing the solution later on. We explore a wide array of design choices to achieve this, in addition to our third goal of high parallel scalability. We present compelling experimental results, demonstrating that our parallel unconstrained local search techniques outperform the prior state of the art by a substantial margin. Compared with four state-of-the-art solvers, our new technique finds 75\% of the best solutions on irregular graphs. We achieve a 9.6\% improvement in edge cut over the next best competitor, while being only 7.7\% slower in the geometric mean.

翻译：我们针对平衡图划分问题提出了新的细化启发式方法，该方法突破了一条历史悠久的规则。传统局部搜索仅允许保持块大小平衡（低于大小约束）的移动。在本工作中，我们证明允许较大的临时平衡违规可显著提升解质量，该效应对社交网络等非规则实例尤为突出。实现这一通用思想的高效设计涉及两方面的精细处理：无约束移动候选者的审慎选择，以及后续重新平衡解的算法。为实现这一目标，除了我们的第三目标——高并行可扩展性之外，我们探索了广泛的设计选择。我们展示了令人信服的实验结果，表明并行无约束局部搜索技术大幅领先于现有最优技术。与四种最先进求解器相比，我们的新技术在非规则图上找到了75%的最优解。在几何均值上，我们相较于次优竞争者在边割上实现了9.6%的改进，而速度仅慢7.7%。