computing the quartet distance between general trees

18 CHAPTER 3. EXPERIMENTAL APPROACHbe chosen as root, so that is what one can expect when parsing such data. This is noproblem and in any case, some entry point is needed to access the tree.When initiating the process of implementing the first algorithm in Python, I did nothave deep and substantial knowledge about the requirements each algorithm would askof the data structure used to store and represent the tree. Consequently, I found myselfusing the simple top-down data structure provided by the Python Newick parserdescribed. This worked out all right in my first attempt on implementing the quarticalgorithm, see Sec. 4.1. However, when attacking the other algorithms, that sometimestake an edge-based approach (remember that subtrees are identified by directed edges),it turned out to be insufficient, inexpressible and confusing.Therefore, enriching the data structure with some constructs that correspond to theideas used in the algorithms, seemed obvious. As long as the modifications could bedone in linear time by simple traversal of the tree, the overhead would easily fit into thetime bounds of the algorithms considered in this thesis.One improvement was to decorate the tree with more directed edges. A recursivedescent parser built using the Toy Parser Generator framework is tail recursive and doesnot leave the opportunity to send back information through the recursion. The result isthat trees parsed with a TPG parser do not have back-edges, i.e. edges pointing towardsthe root. Subsequently adding back-edges, made it easy to traverse the tree from anychoice of start node and in any direction. Also, after realising that the algorithms mostoften deal with directed edges, I let each edge know its opposite and thus two directededges together correspond to one actual undirected edge. The algorithms naturally requireunique identification of leaves and use the assumption that internal nodes andedges can be identified uniquely as well. Therefore, ids were also added in a subsequenttraversal of the tree. Because I implemented the C++ parser and data structure with thisin mind, I made the C++ parser a bit more advanced, letting it add the necessary edgeswhile parsing, keep track of the ids of nodes and edges and collect nodes and edges inlists for easy access. Of course this required that procedures return information aboutthe part of the tree just parsed (the subtree below).The few dissimilarities in the two data structures used are not playing a significantrole in the implementations. There is a slight difference in the way a tree is traversed,since an internal node in the Python data structure has a parent and a number of subtrees,whereas the C++ data structure simply has a number of subtrees related. Furthermore,the fact that the two implementations do the job in different orders result in theedges having different ids in the two languages which will change the order of processingfor edges. This should not have any impact on the results of the algorithms however.