🤖 AI Summary
Balanced graph partitioning for irregular graphs (e.g., social networks) remains challenging due to the strict constraint of maintaining block-size balance during local search.
Method: This work relaxes this constraint by introducing an unconstrained node-movement strategy that permits significant temporary imbalance. It systematically validates that controlled, transient imbalance improves solution quality; designs a heuristic candidate-node selection scheme and a dynamic imbalance control mechanism; and develops a multi-stage, highly parallelized rebalancing algorithm.
Contribution/Results: Evaluated on standard benchmarks, the method achieves solutions within 75% of the optimal objective value, reduces edge-cut ratio by 9.6% over the second-best approach, and incurs only a 7.7% geometric mean runtime overhead—demonstrating both high solution quality and strong scalability.
📝 Abstract
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.