We propose a model for online graph problems where algorithms are given access to an oracle that predicts (e.g., based on modeling assumptions or 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：我们为在线图表问题提出一个模型,让算法能够访问一个预测图中节点度的预想值(例如,基于模型假设或过去的数据)的星标。在这个模型中,我们研究了在线双部匹配和自然贪婪匹配的典型问题,名为MinPredidedDegree,使用离线节点度的预测。对于由于钟、卢和武丘而获得的双方版本的Stochachicato 图形模型的预期值,用来预测图中显示(例如,根据模型假设或过去的数据)节点的节点。在这个模型中,我们研究了在线双方版本的在线离线度预期值的预期值(例如,根据模型或根据以往的数据),我们显示MinprepedDegre Stochest 支配了任何其他在线算法,也就是说,对于从此模型中绘制的图表是最佳的。由于模型的“对称性”版本,所有在线节点都是一样的,因此,对于“已知的i.i.d.d.d.模型”的双方版本,对于此类投入的在线匹配值的相对比率为至少0.299。 对于这种图表,我们经常显示最深层的底的图表,显示最深层的伸缩的伸缩的伸缩的伸缩图,以显示为真实的伸缩的伸缩的伸缩的伸缩,显示的伸缩的伸缩图图,显示,以显示的伸缩的伸缩的伸缩的伸缩的伸缩的伸缩的伸缩的伸缩的伸缩的伸伸缩图,以显示为正的伸伸伸伸伸伸伸伸缩。
相关内容
微信扫码咨询专知VIP会员