Networked bubble propagation method as a polynomial‐time hypothetical reasoning for computing near‐optimal solution

Abstract

AbstractHypothetical reasoning is important to knowledge system framework due to both its theoretical basis and its usefulness in solving practical problems including diagnosis, design, etc. One crucial problem with hypothetical reasoning is, however, its slow inference speed. To achieve practical or tractable speed, an approximate solution method of 0–1 integer programming named Pivot and Complement has been applied so far to a cost‐based hypothetical reasoning, in which a numerical weight is assigned to each possible element hypothesis and an optimal solution hypothesis‐set with the minimal sum of its element hypotheses' weights is searched. In this method, all described knowledge is regarded as constraints. Then, the restricted part of knowledge is transformed into inequalities to apply 0–1 integer programming. While the computational complexity of hypothetical reasoning is NP‐complete or NP‐hard, an approximate solution method of 0–1 integer programming allows polynomial inference time in the order of N4 for finding a near‐optimal solution hypothesis, where N is the number of possible element hypotheses.In this paper, in order to understand the mechanism of the foregoing method from the viewpoint of knowledge processing, it is reformalized using a new type of knowledge network. Our new networked method, name Networked Bubble Propagation is shown to have a similar (or superior) performance to the aforementioned one, i.e., the solutions it obtains are as good as those found with the Pivot and Complement method and the inference time is in the order of N2. This speed‐up is an advantage of considering the knowledge structure of a given problem, thanks to the network.