An improved node mapping algorithm for the cophylogeny reconstruction problem

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

“…This is not the case for the Improved Node Mapping algorithm, however, due to its preprocessing requirement of only linear time and space (Drinkwater and Charleston, 2014a).…”

“…Although previous research has identified that mapping algorithms may not require linear mapping sites to be considered (Drinkwater and Charleston, 2014a), no prior analysis has proven any bound less than O(n).…”

“…It has previously been shown that the subsolutions constructed for the leaves of the parasite tree, subsolutions at level 0, only require O(1) space (Drinkwater and Charleston, 2014a). As the algorithm continues to map parasite nodes into the host tree, the required space incrementally increases for each level of the parasite tree.…”

“…As the algorithm continues to map parasite nodes into the host tree, the required space incrementally increases for each level of the parasite tree. The amount of space increases until it will require O(n) space for the set of mapping sites for each subsolution (Drinkwater and Charleston, 2014a). The proposed data structure takes advantage of the rate at which the number of mapping sites increases, to allow for a subquadratic space solution for the cophylogeny reconstruction problem where the internal node ordering is fixed.…”

“…This approach has been shown to be effective, as solving the cophylogeny reconstruction problem where the internal node ordering is fixed can be solved in polynomial time (Libeskind-Hadas and Charleston, 2009). The initial implementation, known as Node Mapping, ran in O(n 7 ) (Conow et al, 2010), but has been subsequently replaced by Edge Mapping (Yodpinyanee et al, 2011), Slicing (Doyon et al, 2011a,b) and Improved Node Mapping (Drinkwater and Charleston, 2014a), all running in cubic time. Of this set of cubic time algorithms, Edge Mapping and Improved Node Mapping offer the best space complexity as both require only quadratic space (Yodpinyanee et al, 2011;Drinkwater and Charleston, 2014a) as opposed to Slicing which requires cubic space (Doyon et al, 2011a,b).…”