Parameterized Algorithms for Minimum Tree Cut/Paste Distance and Minimum Common Integer Partition

We study two NP-hard problems formulated in computational biology. The minimum tree cut/paste distance problem asks for the minimum number of cut/paste operations we need to apply to transform a tree to another tree. The minimum common integer partition problem asks for a minimum-cardinality integer partition of a number that refines two given integer partitions of the same number. We give parameterized algorithms for both problems.