In this paper, we study the parallel query complexity of reconstructing biological and digital phylogenetic trees from simple queries involving their nodes. This is motivated from computational biology, data protection, and computer security settings, which can be abstracted in terms of two parties, a responder, Alice, who must correctly answer queries of a given type regarding a degree-d tree, T, and a querier, Bob, who issues batches of queries, with each query in a batch being independent of the others, so as to eventually infer the structure of T. We show that a querier can efficiently reconstruct an n-node degree-d tree, T, with a logarithmic number of rounds and quasilinear number of queries, with high probability, for various types of queries, including relative-distance queries and path queries. Our results are all asymptotically optimal and improve the asymptotic (sequential) query complexity for one of the problems we study. Moreover, through an experimental analysis using both real-world and synthetic data, we provide empirical evidence that our algorithms provide significant parallel speedups while also improving the total query complexities for the problems we study.

中文翻译：

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并行重建生物和数字系统发育树

在本文中，我们研究了从涉及节点的简单查询重建生物和数字系统发育树的并行查询复杂性。这源于计算生物学、数据保护和计算机安全设置，可以将其抽象为两方，响应者 Alice，必须正确回答关于度 d 树的给定类型的查询，T 和查询者 Bob 发出批量查询，批处理中的每个查询都独立于其他查询，从而最终推断出 T 的结构。我们证明查询者可以有效地重建 n 节点度数树 T ，具有对数轮数和拟线性查询数，对于各种类型的查询，包括相对距离查询和路径查询，概率很高。我们的结果都是渐近最优的，并提高了我们研究的问题之一的渐近（顺序）查询复杂性。此外，通过使用真实世界和合成数据的实验分析，我们提供了经验证据，证明我们的算法提供了显着的并行加速，同时还提高了我们研究的问题的总查询复杂度。