Figure 3

Search space of pathway prediction and A* algorithm for shortest path search. (A) The metabolic pathway prediction problem between compounds can be replaced by a mathematical shortest path search problem. That is, finding the shortest path to reach the integer vector of a goal compound by adding the integer vectors of reaction rules to the integer vectors of intermediate compounds can be considered a shortest path problem in an integer-vector space. (B) In the A* algorithm, the evaluation function (the distance-plus-cost heuristic) f(t) for each node t in the search space is defined as the sum of two functions: the past-cost function p(t), which is the cost (distance) it has taken to get from the starting node to the current node t, and a heuristic estimate h'(t) of the distance to the goal.