Shortest Beer Path Queries in Outerplanar Graphs
Joyce Bacic, Saeed Mehrabi, Michiel Smid

TL;DR
This paper introduces an efficient data structure for answering shortest beer path queries in outerplanar graphs, enabling rapid retrieval of path weights and paths with optimal preprocessing.
Contribution
It presents a linear-time preprocessing method for outerplanar beer graphs that supports fast shortest beer path queries, improving over previous approaches.
Findings
Preprocessing time is O(n) for outerplanar beer graphs.
Query time for shortest beer path weight is O(α(n)).
Query time for retrieving the shortest beer path is proportional to its length.
Abstract
A \emph{beer graph} is an undirected graph , in which each edge has a positive weight and some vertices have a beer store. A \emph{beer path} between two vertices and in is any path in between and that visits at least one beer store. We show that any outerplanar beer graph with vertices can be preprocessed in time into a data structure of size , such that for any two query vertices and , (i) the weight of the shortest beer path between and can be reported in time (where is the inverse Ackermann function), and (ii) the shortest beer path between and can be reported in time, where is the number of vertices on this path. Both results are optimal, even when is a beer tree (i.e., a beer graph whose underlying graph is a tree).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
