, Volume 60, Issue 2, pp 109-119

Spanning trees and shortest paths in monge graphs

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Abstract

We investigate three problems onMonge graphs, i.e. complete, undirected weighted graphs whose distance matrix is a Monge matrix: (A) the minimum spanning tree problem, (B) the problem of computing all-pairs shortest paths and (C) the problem of determining a minimum weighted 1-to-all shortest path tree. For all three problems best possible algorithms (in terms of complexity) are presented.

This research has been supported by the Spezialforschungsbereich F 003 ‘Optimierung und Kontrolle’/Projektbereich Diskrete Optimierung.