Background: Cophylogeny mapping is used to uncover deep coevolutionary associations between two or more phylogenetic histories at a macro coevolutionary scale. As cophylogeny mapping is NP-Hard, this technique relies heavily on heuristics to solve all but the most trivial cases. One notable approach utilises a metaheuristic to search only a subset of the exponential number of fixed node orderings possible for the phylogenetic histories in question. This is of particular interest as it is the only known heuristic that guarantees biologically feasible solutions. This has enabled research to focus on larger coevolutionary systems, such as coevolutionary associations between figs and their pollinator wasps, including over 200 taxa. Although able to converge on solutions for problem instances of this size, a reduction from the current cubic running time is required to handle larger systems, such as Wolbachia and their insect hosts. 

Results: Rather than solving this underlying problem optimally we present a greedy algorithm called TreeCollapse, which uses common topological patterns to recover an approximation of the coevolutionary history where the internal node ordering is fixed. This approach offers a significant speed-up compared to previous methods, running in linear time. This algorithm has been applied to over 100 well-known coevolutionary systems converging on Pareto optimal solutions in 68% of test cases, where in some cases the reported solution has not previously been recoverable. Further, while TreeCollapse applies a local search technique, it can guarantee solutions are biologically feasible, making this the fastest method to provide such a guarantee. 

Conclusion: As a result, we argue that the newly proposed algorithm is a valuable addition to the field of coevolutionary research. Not only does it offer a significantly faster method for recovering cophylogeny mappings but by using this approach, in conjunction with existing heuristics, it can assist in recovering a larger subset of the Pareto front than has previously been possible.