computing the quartet distance between general trees

Appendix APreprocessing for the sub-cubicalgorithmIn this appendix I will list the details of the preprocessing steps omitted in the descriptionof the sub-cubic algorithm in Chap. 7. Though crucial to the running time of thecomplete algorithm, they do not support the reader in obtaining an overview, and thus,I have chosen to hide them away here.Recall from Sec. 7.1.1 the matrix I which is storing a subset of the table of shared leafset sizes between two trees. All remaining preprocessing arrays and tables are results offurther processing the information in I . Since the information is making little sense byitself, the naming conventions have been kept simple and are not very explanatory.Row and column sums and the sum of all entries of I :R[i ] =d v ′∑j =1I [i , j ]∑d vC [j ] = I [i , j ]M =i=1∑d v d v ′∑i=1 j =1I [i , j ](A.1)(A.2)(A.3)Another matrix I ′ , its row sums, column sums and its total sum of entries:I ′ [i , j ] = I [i , j ](M − R[i ] −C [j ] + I [i , j ])R ′ [i ] =d v ′∑j =1I ′ [i , j ](A.4)(A.5)69