Balanced and swap-robust minimal trades, introduced in [1], are important for studying the balance and stability of server access request protocols under data popularity changes. Constructions of such trades have so far relied on paired sets obtained through iterative combining of smaller sets that have provable stability guarantees, coupled with exhaustive computer search. Currently, there exists a nonnegligible gap between the resulting total dynamic balance discrepancy and the known theoretical lower bound. We present both new upper and lower bounds on the total service requests discrepancy under limited popularity changes. Our constructive near-optimal approach uses a new class of paired graphs whose vertices are two balanced sets with edges (arcs) that capture the balance and potential balance changes induced by limited-magnitude popularity changes (swaps).

翻译：平衡且交换鲁棒的最小交易集（由文献[1]提出）对于研究数据中心请求协议在数据流行度变化下的平衡性与稳定性具有重要意义。此类交易集的构造长期依赖通过迭代组合具有可验证稳定性保证的小规模集合获得的配对集，并结合穷举式计算机搜索。当前，所得总动态平衡偏差与已知理论下界之间存在不可忽略的差距。我们针对有限流行度变化下的总体服务请求偏差提出了新的上界与下界。本文提出的构造性近优方法采用了一类新型配对图，其顶点由两个平衡集合构成，边（弧）则捕获了由有限幅度流行度变化（交换操作）所引致的平衡态及其潜在变化。