title: Towards sub-quadratic time and space complexity solutions for the dated tree reconciliation problem.
abstract: BACKGROUND
  Recent coevolutionary analysis has considered tree topology as a means to reduce the asymptotic complexity associated with inferring the complex coevolutionary interrelationships that arise between phylogenetic trees. Targeted algorithmic design for specific tree topologies has to date been highly successful, with one recent formulation providing a logarithmic space complexity reduction for the dated tree reconciliation problem.
  
  
  METHODS
  In this work we build on this prior analysis providing a further asymptotic space reduction, by providing a new formulation for the dynamic programming table used by a number of popular coevolutionary analysis techniques. This model gives rise to a sub quadratic running time solution for the dated tree reconciliation problem for selected tree topologies, and is shown to be, in practice, the fastest method for solving the dated tree reconciliation problem for expected evolutionary trees. This result is achieved through the analysis of not only the topology of the trees considered for coevolutionary analysis, but also the underlying structure of the dynamic programming algorithms that are traditionally applied to such analysis.
  
  
  CONCLUSIONS
  The newly inferred theoretical complexity bounds introduced herein are then validated using a combination of synthetic and biological data sets, where the proposed model is shown to provide an [Formula: see text] space saving, while it is observed to run in half the time compared to the fastest known algorithm for solving the dated tree reconciliation problem. What is even more significant is that the algorithm derived herein is able to guarantee the optimality of its inferred solution, something that algorithms of comparable speed have to date been unable to achieve.
authors.affiliation: School of Information Technologies, University of Sydney, 1 Cleveland St, Sydney, 2006 NSW Australia.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Drinkwater
authors.affiliation: School of Information Technologies, University of Sydney, 1 Cleveland St, Sydney, 2006 NSW Australia ; School of Physical Sciences, University Of Tasmania, Hobart, 7005 Tasmania Australia.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Charleston
keywords: Coevolution; Cophylogeny; NP-hard; Phylogny; Tree reconciliation; Tree shape