A constructive algorithm for realizing a distance matrix

The natural metric of a weighted graph is the length of the shortest paths between all pairs of vertices. The investigated problem consists in a representation of a given metric by a graph, such that the total length of the graph is minimized. For that purpose, we give a constructive algorithm based on a technique of reduction, fusion and deletion. We then show some results on a set of various distance matrices whose optimal realization is known. Key words: metrics, reduction, heuristics 1991 MSC: 68R05, 05C10, 05C12, 05C50, 05C62

• Type: Journal
• Year: 2006
• Where: EOR
• Authors: Sacha C. Varone
• Keywords: EOR 2006, Investigated Problem, Shortest Paths, Weighted Graph