Reconstructing Biological and Digital Phylogenetic Trees in Parallel

TL;DR

This paper develops parallel algorithms for efficiently reconstructing biological and digital phylogenetic trees using simple queries, achieving asymptotically optimal query complexity and demonstrating significant speedups through experiments.

Contribution

It introduces parallel query algorithms for tree reconstruction that are asymptotically optimal and outperform previous sequential methods.

Findings

Logarithmic rounds and quasilinear queries suffice for reconstruction

Algorithms are asymptotically optimal in query complexity

Experimental results show significant parallel speedups and efficiency improvements

Abstract

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.