Between G Eneral T Rees : a N Experimental Study of a Sub - Cubic Algorithm
نویسندگان
چکیده
This thesis provides strong evidence that the quartet distance between two general trees is practically computable in sub-cubic time. The thesis comprises a detailed study of three algorithms for quartet distance computation between trees of arbitrary degree; a quartic, a cubic and a sub-cubic time algorithm. A common property to these three algorithms is that they all have a time complexity that is only dependent on the number of leaves in the two trees compared and not on the degree of internal nodes. Focus is on the sub-cubic algorithm suggested by Mailund et al. [14] that is currently the theoretically best algorithm in this category and has a time complexity of O(n2+α) where α has a direct dependence on matrix multiplication. This dependence might show to be a problematic obstacle in practice since the need for sub-cubic matrix multiplication is inescapable. The goal is to reveal the practical behavior of the algorithm. Naturally this is done through experimental verification using a wide range of input trees with different properties. The result is clear – the performance of the algorithm is close to quadratic for most input, however, some inputs reveal that the running time is dominated by that of matrix multiplication for very large inputs. Among the contributions of the thesis are: A verification of the correctness and running time of the two reference algorithms including a minor but essential correction of the cubic algorithm. Verification of the correctness of the sub-cubic algorithm leading to a few algorithmic observations that are crucial to obtain a correct result. Practical verification of the theoretical bounds on the time complexity of the sub-cubic algorithm including a discussion of a possibly tighter upper bound. Detailed documentation of the experimental approach with description of the steps necessary to implement the algorithms and reproduce the experiments. Finally, the result is a piece of software that is efficient in practice and has already shown its worth at the time of writing.
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تاریخ انتشار 2010