We propose a model for online graph problems where algorithms are given access to an oracle that predicts (e.g., based on past data) the degrees of nodes in the graph. Within this model, we study the classic problem of online bipartite matching, and a natural greedy matching algorithm called MinPredictedDegree, which uses predictions of the degrees of offline nodes. For the bipartite version of a stochastic graph model due to Chung, Lu, and Vu where the expected values of the offline degrees are known and used as predictions, we show that MinPredictedDegree stochastically dominates any other online algorithm, i.e., it is optimal for graphs drawn from this model. Since the "symmetric" version of the model, where all online nodes are identical, is a special case of the well-studied "known i.i.d. model", it follows that the competitive ratio of MinPredictedDegree on such inputs is at least 0.7299. For the special case of graphs with power law degree distributions, we show that MinPredictedDegree frequently produces matchings almost as large as the true maximum matching on such graphs. We complement these results with an extensive empirical evaluation showing that MinPredictedDegree compares favorably to state-of-the-art online algorithms for online matching.
翻译:我们为在线图形问题提出一个模型,让算算算法能够访问预测(例如,基于过去数据)图中节点的大小。 在这个模型中,我们研究在线双部匹配和自然贪婪匹配的典型问题,即名为 MinPredededDegree 的典型问题,使用离线节点度的预测。对于由于钟、卢、卢和Vu而知道并用作预测的离线度预期值的预值用来预测的星质(例如,根据过去的数据),我们提出一个模型的在线图形问题模型的模型模型模型模型模型模型,使用对离线节点节点节点的度的预测。对于由于钟、卢、卢和Vu而知道并用离线度的预期值来预测的双点模型,我们显示,MinPrepredicreddictedd.d.d.模型的预期离线度值至少为0.7299;关于拥有从此模型的在线图表的特殊案例,即具有最大法律程度分布的经常显示图表,因此,我们展示这些结果的MPre,我们展示了这些结果。