Faster Treewidth-based Approximations for Wiener Index
Résumé
The Wiener index of a graph $G$ is the sum of distances between all pairs of its vertices. It is a widely-used graph property in chemistry, initially discovered to examine the link between the boiling points and structural properties of alkanes, but later found notable applications in drug design. Thus, computing or approximating the Wiener index of molecular graphs, i.e.~graphs in which every vertex models an atom of a molecule and every edge models a bond, is of significant interest to the computational chemistry community.
In this work, we build upon the observation that molecular graphs are sparse and tree-like and focus on developing efficient algorithms, parameterized by treewidth, to approximate the Wiener index. We present a new randomized approximation algorithm using a combination of tree decomposition and centroid decomposition. Our algorithm approximates the Wiener index within a multiplicative factor of $(1+\epsilon)$ in time $O(n \cdot \log{n} \cdot k^3 + \sqrt{n} \cdot \log{n} \cdot (\log{\log{n}} + k )/\epsilon^2)$, where $n$ is the number of vertices of the graph, $k$ is the treewidth, and $\epsilon$ is the error of approximation. Note that the time bound is almost-linear in $n$.
Finally, we provide experimental results over the standard benchmark molecules from PubChem and the Protein Data Bank, showcasing the applicability and scalability of our approach on real-world chemical graphs and comparing it with the previous state-of-the-art methods.
Origine | Fichiers produits par l'(les) auteur(s) |
---|