Eccentricity queries and beyond using hub labels

Hub labeling schemes are popular methods for computing distances on road networks and other large complex networks, often answering to a query within few microseconds graphs with millions of edges. In this work, we study their algorithmic applications beyond distance queries. Indeed, several implementations hub labels were reported have good practical performances, both in terms pre-processing time maximum label size. There also relevant graph classes which know how compute labelings sublinear quasi linear time. These positive results raise the question what can be computed efficiently given small size as input. We focus eccentricity queries distance-sum queries, versions these problems directed weighted graphs, that is part motivated by importance facility location problems. On negative side, show conditional lower bounds above unweighted undirected sparse via standard constructions from “Fine-grained” complexity. Specifically, under Strong Exponential-Time Hypothesis (SETH), requires Ω(|V|2−o(1)) or Ω(|V|1−o(1)) time, even if input ω(log⁡|V|). However, things take different turn when sublogarithmic every ε>0 there exists δε>0 such following hold, being ≤k: after total O(2δε⋅k⋅|V|1+ε) any vertex O(2δε⋅k⋅|V|ε) Our data structure novel application orthogonal range framework Cabello Knauer (2009) [17]. It applied fast global computation some topological indices. Finally, by-product our approach, fixed class bounded expansion, decide whether diameter an n-vertex at most k fε(k)⋅n1+ε ε>0, “explicit” function fε depends ε considered. This result further empirical evidence many expansion (Demaine et al., 2019 [24]), online social relatively diameter.