A new application of Orthogonal Range Searching for computing Giant Graph Diameters

Guillaume Ducoffe (1, 2)

1 ICI - National Institute for Research and Development in Informatics [Bucharest]
2 Faculty of Mathematics-Informatics

A well-known problem for which it is difficult to improve the textbook algorithm is computing the graph diameter. We present two versions of a simple algorithm (one being Monte Carlo and the other deterministic) that for every fixed h and unweighted undirected graph G with n vertices and m edges, either correctly concludes that diam(G) < hn or outputs diam(G), in time O(m + n^{1+o(1)}). The algorithm combines a simple randomized strategy for this problem (Damaschke, IWOCA'16) with a popular framework for computing graph distances that is based on range trees (Cabello and Knauer, Computational Geometry'09). We also prove that under the Strong Exponential Time Hypothesis (SETH), we cannot compute the diameter of a given n-vertex graph in truly subquadratic time, even if the diameter is an Θ(n/ log n).

Mots clés: Graph diameter; Orthogonal Range Queries; Hardness in P; FPT in P

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

Guillaume Ducoffe. A new application of Orthogonal Range Searching for computing Giant Graph Diameters. 2nd Symposium on Simplicity in Algorithms (SOSA 2019), Jan 2019, San Diego, CA, United States. pp.12:1-12:7, ⟨10.4230/OASIcs.SOSA.2019.12⟩. ⟨hal-01974190⟩