Computational biology is mainly concerned with discovering an object from a given set of observations that are supposed to be good approximations of the real object. Two important steps here are to define a way to measure the distance between different objects and to calculate the distance between two given objects. The main problem is then to find an object that has the minimum total distance to the given observations. 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 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.

计算生物学主要涉及从给定的一组观察中发现一个物体，这些观察被认为是真实物体的良好近似。这里的两个重要步骤是定义一种测量距离的方法并计算两个给定对象之间的距离。然后，主要问题是找到距给定观测值的总距离最小的物体。我们研究在计算生物学中提出的两个NP难题。最小树剪切/粘贴距离问题要求我们将一棵树转换为另一棵树所需的最小剪切/粘贴操作数。最小公共整数分区问题要求一个数字的最小基数整数分区，以细化相同数字的两个给定整数分区。我们针对这两个问题给出了参数化算法。