Bundling all shortest paths

Investor logo


This publication doesn't include Faculty of Medicine. It includes Faculty of Informatics. Official publication website can be found on muni.cz.

DĘBSKI Michał Karol JUNOSZA-SZANIAWSKI Konstanty LONC Zbigniew

Year of publication 2020
Type Article in Periodical
Magazine / Source Discrete Applied Mathematics
MU Faculty or unit

Faculty of Informatics

Web https://doi.org/10.1016/j.dam.2019.08.027
Doi http://dx.doi.org/10.1016/j.dam.2019.08.027
Keywords shortest paths; ALT algorithm
Description We study the problem of finding a minimum bundling set in a graph, where a bundling set is a set B of vertices such that every shortest path can be extended to a shortest path from a vertex in B to some other vertex. If G is a weighted graph, we denote the size of a minimum bundling set in G by b(G). Bundling sets can be used by the ALT algorithm that finds shortest paths in weighted graphs. For a fixed bundling setBin a weighted graph G, after some preprocessing using O(|B||V(G)|) memory, it is possible to determine the distance between any two verticesin time O(|B|). Therefore, it is desirable to find small bundling sets. We show that determining b(G) is NP-hard and give a 2-approximation algorithm. Moreover we characterize simple graphs with b=1 and subgraphs of grids with b=2. We also introduce the parameter b*(G) equal to the minimum of b(H) over all weighted graphs H such that G is an isometric subgraph of H, i.e. for every two vertices u, v of G the distances from u to v in G and in H are the same. Sometimes b*(G) is much smaller than b(G) and a further improvement of performance of route planning can be obtained. As a part of a proof, we show that at least Theta(logn/loglogn) triangle-free graphs are needed to cover a complete graph on n vertices, which may be of independent interest.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info