Abduction is widely used in the task of plan recognition, since it can be viewed as the task of finding the best explanation for a set of observations. The major drawback of abduction is its computational complexity. The task of abductive reasoning quickly becomes intractable as the background knowledge is increased. Recent efforts in the field of computational linguistics have enriched computational resources for commonsense reasoning. The enriched knowledge base facilitates exploring practical plan recognition models in an open-domain. Therefore, it is essential to develop an efficient framework for such large-scale processing. In this paper, we propose an efficient implementation of Weighted abduction. Our framework transforms the problem of explanation finding in Weighted abduction into a linear programming problem. Our experiments showed that our approach efficiently solved problems of plan recognition and outperforms state-of-the-art tool for Weighted abduction.