Shortest Beer Path Queries in Outerplanar Graphs

A beer graph is an undirected G, in which each edge has a positive weight and some vertices have store. path between two u v G any that visits at least one We show outerplanar with n can be preprocessed O(n) time into data structure of size O(n), such for query v, (i) the shortest reported $$O(\alpha (n))$$ (where $$\alpha (n)$$ inverse Ackermann function), (ii) O(L) time, where L number on this path. Note running does not depend G. Both results are optimal, even when tree (i.e., whose underlying tree).