On Inference of a Chemical Structure from Path Frequency

This paper studies the problem of inferring a chemical compound from a feature vector consisting of the numbers of occurrences of vertex-labeled paths, which has potential future applications for designing new chemical compounds based on the kernel methods. This paper shows that the problem for outerplanar graphs of bounded degree can be solved in polynomial time if an alphabet is fixed and the maximum length of paths and the number of edges of each face are bounded by a constant. It is also shown that the problem is strongly NP-hard even for trees of unbounded degree.