A time and space complexity reduction for coevolutionary analysis of trees generated under both a Yule and Uniform model

RASCAL: A Randomized Approach for Coevolutionary Analysis

“…As a result, the time complexity of this algorithm is directly bounded by the number of mapping sites stored for each node p i ∈ P . This result is part of a larger proof which demonstrated that for a subset of tree topologies that asymptotically less than O(n) mapping sites are required to solve the DTR problem optimally [Drinkwater and Charleston, 2015]. It is this characteristic that we aim to further exploit to reduce the time and space complexity bound for the DTR problem using random sampling for all tree topologies.…”

“…This is due to the O(n log n) preprocessing step required for each parasite node which is independent of the number of mapping sites stored. Therefore, while Bansal et al's [2012] solution is more efficient when solving the problem optimally, its design prohibits any asymptotic time complexity decrease by reducing the number of sub solutions that are retained at each iteration [Drinkwater and Charleston, 2015].…”

“…While still possible to use a two-dimensional matrix, this time of size O(kn), we have instead stored the sub solutions within an array of lists. This is due to a recent result showing a logarithmic reduction in running time is possible when using an array of lists for a select subset of tree topologies [Drinkwater and Charleston, 2015]. While this approach does not provide an asymptotic reduction for all tree topologies, it is expected to perform faster in practice compared to using the traditional two dimensional matrix.…”

Towards sub-quadratic time and space complexity solutions for the dated tree reconciliation problem

“…While no single model is able to capture the variation of all evolutionary trees, it is possible to bound this variation using the Yule and Uniform synthetic tree generation models [ 7 , 8 ]. As such, targeted algorithmic development has been able to exploit this narrow subset of expected topologies as a means to optimise phylogenetic analysis techniques for expected evolutionary data [ 9 ].…”

“…Tree topology, however, may be leveraged for such analysis, as coevolution considers the relationships between two or more phylogenetic trees. One popular coevolutionary analysis approach where tree topology may be exploited is cophylogeny mapping , due to the high correlation between this technique’s computational complexity and the shape of phylogenetic trees [ 9 ].…”