带度量权重的在线关联聚类
Online Correlation Clustering with Metric Weights
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中文总结 AI 辅助
本文针对全在线模型中带度量权重的关联聚类，提出首个常数竞争的确定性在线算法，证明边权重的度量一致性可克服标准在线关联聚类的下界难题。
中文摘要 AI 辅助
标准在线关联聚类问题极难，即便随机算法也无法达到优于Ω(n)的竞争比。现有研究通过 recourse（资源调配）、随机到达顺序或用离线输入样本初始化算法来放宽在线模型以规避该下界。本文转而探究输入本身的额外结构能否克服该下界，研究概率约束下的加权关联聚类，其中每条边uv满足w⁺_uv + w⁻_uv = 1，且负权重w⁻满足三角不等式约束。该版本的关联聚类在离线场景中已被广泛研究，本文首次开展其在线研究，提出一种确定性在线算法，该算法在对抗性到达顺序下，能使维护的聚类总加权分歧代价与离线最优值的比值处于O(1)因子范围内。这是全在线模型中关联聚类自然最小化变体的首个常数竞争在线算法，表明边权重的度量一致性可区分在线问题的易处理与难处理实例。
英文摘要
The standard online version of correlation clustering is prohibitively hard, as even randomized algorithms cannot achieve competitive ratio better than $Ω(n)$. Prior works bypass this lower bound by relaxing the online model through recourse, random arrival order, or seeding the algorithm with an offline sample of the underlying input. We instead ask whether additional structure in the input itself can overcome this lower bound. We study weighted correlation clustering under probability constraints, where $w^+_{uv}+w^-_{uv}=1$ for every $uv$ edge, and triangle inequality constraints, where the negative weights $w^-$ satisfy triangle inequality. While this version of correlation clustering is well-studied in the offline setting, we initiate its online study and give a deterministic online algorithm that maintains a clustering whose total weighted disagreement cost is within an $O(1)$ factor of the offline optimum, against adversarial arrival order. This is the first constant-competitive online algorithm for a natural minimization variant of correlation clustering in the fully online model, and shows that metric consistency on the edge weights separates tractable from intractable online instances.
