The Longest Minimum-Weight Path in a Complete Graph

We consider the minimum-weight path between any pair of nodes of the n-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variables. We show that the longest of these minimum-weight paths has about log n edges where 3.5911

• Type: Journal
• Year: 2010
• Where: CPC
• Authors: Louigi Addario-Berry, Nicolas Broutin, Gábor Lugosi
• Keywords: CPC 2010, Minimum-weight Paths, N-vertex Complete Graph, Random Variables