In this paper, we propose a method for estimating meaningful actions from long-term observation of everyday manipulation tasks without prior knowledge as part of an action understanding framework for life support robotic systems. The target task is defined as a sequence of interactions between objects. An interaction that appears many times is assumed to be meaningful and repetitious relative motion patterns are detected from trajectories of multiple objects. The main contribution is that the problem is formulated as a combinatorial optimization problem with two parameters, target object labels and correspondences on similar motion patterns, and is solved using local and global Dynamic Programming (DP) in polynomial time O(N logN), where N is a total amount of data. The proposed method is evaluated against manipulation tasks using everyday objects such as a cup and a tea-pot.