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 91% of the best solutions on irregular graphs. We achieve a 13.8% improvement in edge cut over the next best competitor, while being only 11.4% slower in the geometric mean.

翻译：我们针对平衡图划分问题提出了新的改进启发式方法，打破了长期以来的传统规则。传统局部搜索仅允许保持模块平衡（低于大小约束）的移动。本研究表明，允许较大的临时平衡违规可显著提高解的质量，这种效果在不规则实例（如社交网络）中尤为突出。实现该通用思想的高效设计涉及无约束移动候选的谨慎选择以及后续解的再平衡算法。除实现高并行可扩展性这一第三目标外，我们探索了多种设计选择来实现这一目标。实验结果表明，我们的并行无约束局部搜索技术大幅超越了现有最优方法。与四种最先进的求解器相比，我们的新技术在不规则图上找到了91%的最优解。在边割指标上比次优竞争者改进13.8%，而几何平均耗时仅增加11.4%。