The Longest Minimum-Weight Path in a Complete Graph

• Published in: Combinatorics, probability & computing Vol. 19; no. 1; pp. 1 - 19
• Main Authors: ADDARIO-BERRY, LOUIGI, BROUTIN, NICOLAS, LUGOSI, GÁBOR
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.01.2010

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 α* log n edges, where α* ≈ 3.5911 is the unique solut...